1
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
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 Evening Shift
+4
-1
When radiation of wavelength $$\lambda$$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is :
A
2$$\lambda$$
B
4$$\lambda$$
C
8$$\lambda$$
D
6$$\lambda$$
3
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
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
$${{\ln {3 \over 2}} \over \lambda }$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
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
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