1
BITSAT 2022
+3
-1

In a radioactive material the activity at time t1, is A1 and at a later time t2, it is A2. If the decay constant of the material is $$\lambda$$, then

A
$${A_1} = {A_2}\,{e^{ - \lambda ({t_1} - {t_2})}}$$
B
$${A_1} = {A_2}\,{e^{\lambda ({t_1} - {t_2})}}$$
C
$${A_1} = {A_2}({t_2}/{t_1})$$
D
$${A_1} = {A_2}$$
2
BITSAT 2021
+3
-1

A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $$\lambda$$2 and that of proton is $$\lambda$$1. The ratio $${{{\lambda _2}} \over {{\lambda _1}}}$$ is proportional to

A
E2
B
E$$^{{1 \over 2}}$$
C
E$$-$$1
D
E$$^{ - {1 \over 2}}$$
3
BITSAT 2021
+3
-1

The radius of a muonic hydrogen atom is 2.5 $$\times$$ 10$$-$$13 m. The total atomic volume (in m3) of a mole of such hydrogen atoms is (Take, $$\pi$$ = 3.14)

A
3.94 $$\times$$ 10$$-$$14
B
3.09 $$\times$$ 10$$-$$14
C
4 $$\times$$ 10$$-$$14
D
3.9 $$\times$$ 10$$-$$14
4
BITSAT 2021
+3
-1

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is

A
0.4 loge 2
B
0.2 loge 2
C
0.1 loge 2
D
0.8 loge 2
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