1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Morning Slot

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $$ \times $$ 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :
A
5 days and 10 days
B
10 days and 40 days
C
20 days and 5 days
D
20 days and 10 days

Explanation

Let number of nuclei present in material A is NA and in meterial B is NB According to question,

NA = 2NB

We know, activity (A) = $$\lambda $$N.

$$ \therefore $$   $$\lambda $$ANA = 10 . . . . . . (1)

and $$\lambda $$B NB = 20 . . . . . . . (2)

$$ \therefore $$   By dividing (1) by (2), we get

$${{{\lambda _A}{N_A}} \over {{\lambda _B}{N_B}}}$$ = $${1 \over 2}$$

$$ \Rightarrow $$   $${{{\lambda _A}} \over {{\lambda _B}}} \times 2$$ = $${1 \over 2}$$ [as NA = 2NB]

$$ \Rightarrow $$    $${{{\lambda _A}} \over {{\lambda _B}}}$$ = $${1 \over 4}$$

We know,

T$$_{{1 \over 2}}$$  $$ \propto $$ $${1 \over \lambda }$$

$$ \therefore $$   $${{{{\left( {{T_{{1 \over 2}}}} \right)}_A}} \over {{{\left( {{T_{{1 \over 2}}}} \right)}_B}}}$$ = $${{{\lambda _B}} \over {{\lambda _A}}} = 4$$

$$ \Rightarrow $$   $${\left( {{T_{{1 \over 2}}}} \right)_A}$$ = 4$${\left( {{T_{{1 \over 2}}}} \right)_B}$$

$$ \therefore $$   By checking options you can see possible value of $${\left( {{T_{{1 \over 2}}}} \right)_A}$$ = 20 days and $${\left( {{T_{{1 \over 2}}}} \right)_B}$$ = 5 days
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 9th January Evening Slot

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio $${{{R_B}} \over {{R_A}}}$$ of their activities after time t itself decays with time t as e$$-$$3t. If the half-life of A is ln2, the half-life of B is :
A
4ln2
B
$${{\ln 2} \over 2}$$
C
$${{\ln 2} \over 4}$$
D
2ln2

Explanation

We know,

Activity (R) = R0 e$$-$$$$\lambda $$t

Given that,

at t = 0

RA = RB

$$ \Rightarrow $$  R0A e$$-$$$$\lambda $$Ax0 = R0B e$$-$$ $$\lambda $$Bx0

$$ \Rightarrow $$  R0A = R0B

Given that at time t,

$${{{R_B}} \over {{R_A}}} = {e^{^{ - 3t}}}$$

$$ \Rightarrow $$   $${{{R_{0B}}\,{e^{ - {\lambda _B}t}}} \over {{R_{0A}}\,{e^{ - {\lambda _A}t}}}}$$ = e$$-$$3t

$$ \Rightarrow $$  $${e^{\left( {{\lambda _A} - {\lambda _B}} \right)t}} = {e^{ - 3t}}$$

$$ \Rightarrow $$  ($$\lambda $$A $$-$$ $$\lambda $$B)t = $$-$$3t

$$ \Rightarrow $$ $$\lambda $$A $$-$$ $$\lambda $$B = $$-$$ 3 . . . . . (1)

We know half life, $${t_{{1 \over 2}}} = {{{{\ln }^2}} \over \lambda }$$

$$ \therefore $$  Half life of A is, $${{t_{{1 \over 2}}} = {{{{\ln }^2}} \over {{\lambda _A}}}}$$

$$ \therefore $$  $$\lambda $$A = $${{\ln 2} \over {{t_{{1 \over 2}}}}}$$

= $${{\ln 2} \over {\ln 2}}$$

= 1

From equation (1)     we get,

$$\lambda $$A $$-$$ $$\lambda $$B = $$-$$ 3

$$ \Rightarrow $$  1 $$-$$ $$\lambda $$B = $$-$$ 3

$$ \Rightarrow $$  $$\lambda $$B = 4

$$ \therefore $$  Half life of B is $$\left( {{t_{{1 \over 2}}}} \right) = {{\ln 2} \over {{\lambda _B}}} = {{\ln 2} \over 4}$$
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Morning Slot

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -
A
200
B
150
C
400
D
360

Explanation

at t = 0, A0 = $${{dN} \over {dt}}$$ = 1600C/s

at t = 8s, A = 100 C/s

$${A \over {{A_0}}}$$ = $${1 \over {16}}$$ in 8 sec

Therefor half life is t1/2 = 2 sec

$$ \therefore $$   Activity at t = 6 will be 1600$${\left( {{1 \over 2}} \right)^3}$$

       = 200 C/s
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Evening Slot

Consider the nuclear fission

Ne20 $$ \to $$ 2He4 + C12

Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -
A
8.3 MeV energy will be released
B
energy of 11.9 MeV has to be supplied
C
energy of 12.4 MeV will be supplied
D
energy of 3.6 MeV will be released

Explanation

Ne20      $$ \to $$  2He4 + C12

Q – value, EB = (BE)react $$-$$ (BE)product

= (20 × 8.03) – ((2 × 7.07 × 4) + 7.86 × 12)

= 9.72 MeV

Questions Asked from Atoms and Nuclei

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2002 (3)
keyboard_arrow_right
AIEEE 2003 (9)
keyboard_arrow_right
AIEEE 2004 (3)
keyboard_arrow_right
AIEEE 2005 (5)
keyboard_arrow_right
AIEEE 2006 (5)
keyboard_arrow_right
AIEEE 2007 (4)
keyboard_arrow_right
AIEEE 2008 (2)
keyboard_arrow_right
AIEEE 2009 (2)
keyboard_arrow_right
AIEEE 2010 (3)
keyboard_arrow_right
AIEEE 2011 (2)
keyboard_arrow_right
AIEEE 2012 (3)
keyboard_arrow_right
JEE Main 2013 (Offline) (1)
keyboard_arrow_right
JEE Main 2014 (Offline) (2)
keyboard_arrow_right
JEE Main 2015 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Offline) (2)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Offline) (3)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Evening Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Morning Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Morning Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 22th July Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Morning Shift (2)
keyboard_arrow_right

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

Medical

NEET