iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 25th June Evening Shift
Which of the following figure represents the variation of ${l_n}\left( {{R \over {{R_0}}}} \right)$ with ${l_n}A$ (if R = radius of a nucleus and A = its mass number)
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 24th June Evening Shift
In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :
As electron makes transition to higher level, total energy and potential energy increases (due to negative sign) while the kinetic energy reduces.
2022
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 24th June Morning Shift
Choose the correct option from the following options given below :
A.
In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
B.
An atom has a nearly continuous mass distribution in a Rutherford's model but has a highly non-uniform mass distribution in Thomson's model.
C.
A classical atom based on Rutherford's model is doomed to collapse.
D.
The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.
Correct Answer: C
Explanation:
An atom based on classical theory of Rutherford's model should collapse as the electrons in continuous circular motion that is a continuously accelerated charge should emit EM waves and so should lose energy. These electrons losing energy should soon fall into heavy nucleus collapsing the whole atom.
2022
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 24th June Morning Shift
Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 29th July Evening Shift
Two radioactive materials A and B have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $\frac{1}{a \lambda}$. The value of a is _________.
Correct Answer: 9
Explanation:
$N_{A}=N_{0} e^{-25 \lambda t}$
$N_{B}=N_{0} e^{-16 \lambda t}$
$\frac{N_{B}}{N_{A}}=e=e^{9 \lambda t}$
$t=\frac{1}{9 \lambda}$
2022
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 28th July Morning Shift
A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 26th July Evening Shift
Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :
${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y$
The binding energies per nucleon for $\frac{2}{1} X$ and ${ }_{2}^{4} Y$ are $1.1 \,\mathrm{MeV}$ and $7.6 \,\mathrm{MeV}$ respectively. The energy released in this process is _______________ $\mathrm{MeV}$.
Correct Answer: 26
Explanation:
Energy released = Change in B.E.
(7.6 $\times$ 4) $-$ [4 $\times$ 1.1] = 26 MeV
2022
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 26th July Morning Shift
In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a$\lambda$'' between the wavelength of $3^{\text {rd }}$ transition line of Paschen series and that of $2^{\text {nd }}$ transition line of Balmer series where $\mathrm{a}=$ ___________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 30th June Morning Shift
A hydrogen atom in its first excited state absorbs a photon of energy x $\times$ 10$-$2 eV and excited to a higher energy state where the potential energy of electron is $-$1.08 eV. The value of x is ______________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 29th June Evening Shift
The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 29th June Morning Shift
$\sqrt {{d_1}} $ and $\sqrt {{d_2}} $ are the impact parameters corresponding to scattering angles 60$^\circ$ and 90$^\circ$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For d1 = x d2, the value of x will be ____________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 27th June Morning Shift
A beam of monochromatic light is used to excite the electron in Li+ + from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x $\times$ 10$-$10 m. The value of x is ___________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2022 (Online) 24th June Evening Shift
A sample contains 10$-$2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is ${x \over {100}}$. The value of x is ___________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 1st September Evening Shift
The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :
A.
x-will decay faster than y.
B.
y-will decay faster than x.
C.
x and y have same decay rate initially and later on different decay rate.
D.
x and y decay at the same rate always.
Correct Answer: B
Explanation:
Given, ($\tau$1/2)x = ($\tau$)y
Here, $\tau$1/2 = half-life period of radioactive element and $\tau$ = mean life period of radioactive element.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 31st August Morning Shift
A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :
(Assume that at t = 0, there are no B atoms in the sample)
A.
B.
C.
D.
Correct Answer: D
Explanation:
A $\to$ B $\to$ C (stable)
Initially no. of atoms of B = 0 at t = 0, no. of atoms of B will starts increasing & reaches maximum value when rate of decay of B = rate of formation of B.
After that maximum value, no. of atoms will starts decreasing as growth & decay both are exponential functions, so best possible graph is (d).
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th August Morning Shift
There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $\left( {\sqrt 2 = 1.414} \right)$
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th August Evening Shift
At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of NB(t) / NB(0) with respect to time t?
${N_{{B_{\max }}}}$ at $t = {1 \over {2\lambda }}$
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th August Morning Shift
A particular hydrogen like ion emits radiation of frequency 2.92 $\times$ 1015 Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th July Evening Shift
Consider the following statements :
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below :
A.
A, B, C, D and E
B.
A, B and E only
C.
B and D only
D.
A, C and E only
Correct Answer: B
Explanation:
(A) True, atom of each element emits characteristic spectrum.
(B) True, according to Bohr's postulates $mvr = {{nh} \over {2\pi }}$ and hence electron resides into orbits of specific radius called stationary orbits.
(C) False, density of nucleus is constant.
(D) False, A free neutron is unstable decays into proton and electron and antineutrino.
(E) True, unstable nucleus show radioactivity.
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th July Morning Shift
If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th July Morning Shift
Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th July Morning Shift
The half-life of ${}^{198}Au$ is 3 days. If atomic weight of ${}^{198}Au$ is 198 g/mol then the activity of 2 mg of ${}^{198}Au$ is [in disintegration/second] :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 22th July Evening Shift
A nucleus with mass number 184 initially at rest emits an $\alpha$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the $\alpha$-particle.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 20th July Evening Shift
For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :
A.
9.15 sec
B.
6.93 sec
C.
2.62 sec
D.
4.62 sec
Correct Answer: D
Explanation:
R = R0e$-$$\lambda$t
lnR = lnR0 $-$ $\lambda$t
$-$$\lambda$ is slope of straight line
$\lambda$ = ${3 \over {20}}$
${t_{1/2}} = {{\ln 2} \over \lambda } = 4.62$
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 20th July Morning Shift
A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1)
A.
740 years
B.
1110 years
C.
700 years
D.
340 years
Correct Answer: A
Explanation:
The given situation can be shown as
Here, radioactive material X is decayed into two particles Y and Z with their respective decay constant, $\lambda$a and $\lambda$b. It means that
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 18th March Evening Shift
The decay of a proton to neutron is :
A.
always possible as it is associated only with $\beta$+ decay
B.
possible only inside the nucleus
C.
not possible as proton mass is less than the neutron mass
D.
not possible but neutron to proton conversation is possible
Correct Answer: B
Explanation:
Positron emission or Beta plus decay is a subtype of radioactive decay called Beta decay, in which a proton inside a nucleus is converted into a neutron while releasing a positron and an electron neutrino.
So, decay of a proton to neutron is possible only inside the nucleus. Free proton cannot decay to neutron as mass of proton is less compared to neutron so to decay into higher mass, proton need extra energy which free proton can’t get, only proton inside nucleus can get.
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 18th March Morning Shift
Imagine that the electron in a hydrogen atom is replaced by a muon ($\mu$). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :
A.
13.6 eV
B.
2815.2 eV
C.
331.2 eV
D.
27.2 eV
Correct Answer: B
Explanation:
mm = 207 me
In hydrogen atom one electron present. Now that the electron in hydrogen atom is replaced by a muon ($\mu$).
We know, Energy(E) = $ - {{{e^4}m} \over {8\varepsilon _0^2{n^2}{h^2}}}$
For electron,
Ee = $ - {{{e^4}{m_e}} \over {8\varepsilon _0^2{n^2}{h^2}}}$ = 13.6 eV
For muon,
Em = $ - {{{e^4}\left( {207} \right){m_e}} \over {8\varepsilon _0^2{n^2}{h^2}}}$
= 13.6 $ \times $ 207 = 2815.2 eV
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 18th March Morning Shift
A radioactive sample disintegrates via two independent decay processes having half lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life T1/2 of the nuclei is :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th February Evening Shift
A radioactive sample is undergoing $\alpha$ decay. At any time t1, its activity is A and another time t2, the activity is ${A \over 5}$. What is the average life time for the sample?
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 26th February Morning Shift
If $\lambda$1 and $\lambda$2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $\lambda$1 : $\lambda$2 is :
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th February Evening Shift
The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :
A.
194.8 nm
B.
490.7 nm
C.
913.3 nm
D.
121.8 nm
Correct Answer: D
Explanation:
$\Delta$E = 10.2 eV
${{hc} \over \lambda }$ = 10.2 eV
$\lambda$ = ${{hc} \over {(10.2)e}}$
= ${{12400} \over {10.2}}\mathop A\limits^o $
= 121.56 nm
$ \simeq $ 121.8 nm
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th February Morning Shift
Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio ${{{N_1}} \over {{N_2}}}$ will be equal to :
A.
${1 \over 8}$
B.
${3 \over 1}$
C.
${1 \over 3}$
D.
${8 \over 1}$
Correct Answer: D
Explanation:
Let Half life of x = t
then half life of y = 2t
when 3 half life of y is completed then 6 half life of x is completed.
$ \therefore $ Now x have = ${{{N_1}} \over {{2^6}}}$ nuclei
$\therefore$ Frequency will be maximum for transition n = 2 to n = 1.
2021
JEE Mains
MCQ
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 24th February Morning Shift
In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.
The transitions A, B and C respectively represent :
A.
The series limit of Lyman series, second member of Balmer series and second member of Paschen series.
B.
The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.
C.
The series limit of Lyman series, third member of Balmer series and second member of Paschen series.
D.
The first member of the Lyman series, third member of Balmer series and second member of Paschen series.
Correct Answer: C
Explanation:
In transition A, hydrogen atom comes from higher energy state n = $\infty$ to lower energy state n = 1. Hence, transition A represents series limit of Lyman series. In transition B, hydrogen atom comes from higher energy state n = 5 to lower energy state n = 2. Hence, transition B represents 3rd line of Balmer series. In transition C, hydrogen atom comes from higher energy state n = 5 to lower energy state n = 3. Hence, transition C represents 2nd line of Paschen series.
Hence, option (c) is correct.
2021
JEE Mains
Numerical
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th August Evening Shift
X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The value of X is ______________.
Correct Answer: 15
Explanation:
No. of different wavelengths = ${{n(n - 1)} \over 2}$
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th July Evening Shift
The K$\alpha$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be __________ keV. (Round off to the nearest integer)
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th July Morning Shift
In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $\mathop A\limits^o $. If the speed of electron is 2.2 $\times$ 166 m/s, then the current associated with the electron will be _____________ $\times$ 10$-$2 mA. [Take $\pi$ as ${{22} \over 7}$]
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 27th July Morning Shift
A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $\mu$F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _____________ $\Omega$.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 25th July Evening Shift
The nuclear activity of a radioactive element becomes ${\left( {{1 \over 8}} \right)^{th}}$ of its initial value in 30 years. The half-life of radioactive element is _____________ years.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 20th July Evening Shift
A radioactive substance decays to ${\left( {{1 \over {16}}} \right)^{th}}$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.
iCON Education HYD, 79930 92826, 73309 72826JEE Main 2021 (Online) 17th March Evening Shift
A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditions are applied, radii of possible orbitals rn vary with ${n^{{1 \over \alpha }}}$, where $\alpha$ is ____________.
Correct Answer: 3
Explanation:
$\overrightarrow F = - {{d\overrightarrow u } \over {dr}}$
