1
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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 :

[$$\lambda$$ is the radioactive decay constant]
A
$$-$$ $$\lambda$$ (1 $$-$$ e$$-$$$$\lambda$$t)
B
$$\lambda$$ (1 $$-$$ e$$-$$$$\lambda$$t)
C
$$\lambda$$e$$-$$$$\lambda$$t
D
$$-$$ $$\lambda$$e$$-$$$$\lambda$$t
2
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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 :

(where $$\lambda$$ is the decay constant)
A
$${1 \over 2}{{\ln 2} \over \lambda }$$
B
$${{\ln 2} \over \lambda }$$
C
$${{2\ln 2} \over \lambda }$$
D
$${{\ln {3 \over 2}} \over \lambda }$$
3
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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] :
A
2.67 $$\times$$ 1012
B
6.06 $$\times$$ 1018
C
32.36 $$\times$$ 1012
D
16.18 $$\times$$ 1012
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
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.
A
5.5 MeV
B
5.0 MeV
C
5.38 MeV
D
0.12 MeV
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