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Question

A radioactive nucleus can decay by three different processes simultaneously. The half life for the processes are $1 h, \frac{1}{2} h, \frac{1}{2} h$ . The effective half life of the nucleus is

$(1 + \frac{1}{2} + \frac{1}{2}) h o u r$

$(\frac{3 - 2}{7}) h o u r$

$\frac{1}{2 2} h o u r$

$\frac{3 + 2}{7} h o u r$

$\frac{1}{2} h o u r$

Hard

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Updated on : 2022-09-05

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Correct option is B)

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(a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus.
(b) How is the mean life of a given radioactive nucleus related to the decay constant?

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A radioactive nucleus can decay by two different processes. The mean value period for the first process is $t_{1}$ and that for the second process is $t_{2}$ . The effective mean value period for the two processes is

Medium

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Knowing the decay constant $λ$ of a nucleus, find
(a) the probability of decay of the nucleus during the time from $0$ to $t$ ;
(b) the mean lifetime $τ$ of the nucleus.

Hard

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half life of a radioactive substance A is 4 days. the probability that a nucleus will decay in two half lives is:

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The decay constant of a radioactive sample is $λ$ . The respective values of its half life and meanlife are
i) $\frac{1}{λ}$ and $(l o g_{e} 2)$
ii) $\frac{l o g _{e} 2}{λ}$ and $\frac{1}{λ}$

Medium

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Practice more questions

A radioactive nucleus can decay by three different processes simultaneously. The half life for the processes are 1h,2​1​h,21​h. The effective half life of the nucleus is

(1+2​1​+21​)hour

(73−2​​)hour

22​1​hour

73+2​​hour

21​hour

(a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus. (b) How is the mean life of a given radioactive nucleus related to the decay constant?

A radioactive nucleus can decay by two different processes. The mean value period for the first process is t1​ and that for the second process is t2​. The effective mean value period for the two processes is

Knowing the decay constant λ of a nucleus, find (a) the probability of decay of the nucleus during the time from 0 to t; (b) the mean lifetime τ of the nucleus.

half life of a radioactive substance A is 4 days. the probability that a nucleus will decay in two half lives is:

The decay constant of a radioactive sample is λ. The respective values of its half life and meanlife are i) λ1​ and (loge​2) ii) λloge​2​ and λ1​

Revise with Concepts

Law of Radioactive Decay

Plot Number of Neutrons vs Protons for Radioactive Decay

Half Life

A radioactive nucleus can decay by three different processes simultaneously. The half life for the processes are $1 h, \frac{1}{2} h, \frac{1}{2} h$ . The effective half life of the nucleus is

$(1 + \frac{1}{2} + \frac{1}{2}) h o u r$

$(\frac{3 - 2}{7}) h o u r$

$\frac{1}{2 2} h o u r$

$\frac{3 + 2}{7} h o u r$

$\frac{1}{2} h o u r$

(a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus.
(b) How is the mean life of a given radioactive nucleus related to the decay constant?

A radioactive nucleus can decay by two different processes. The mean value period for the first process is $t_{1}$ and that for the second process is $t_{2}$ . The effective mean value period for the two processes is

Knowing the decay constant $λ$ of a nucleus, find
(a) the probability of decay of the nucleus during the time from $0$ to $t$ ;
(b) the mean lifetime $τ$ of the nucleus.

The decay constant of a radioactive sample is $λ$ . The respective values of its half life and meanlife are
i) $\frac{1}{λ}$ and $(l o g_{e} 2)$
ii) $\frac{l o g _{e} 2}{λ}$ and $\frac{1}{λ}$