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The relationship between decay constant ...

The relationship between decay constant `lamda` and half-life T of a radioactive substance is

A

`lamda=(log_(10)2)/(T)`

B

`lamda=(log_(e)2)/(T)`

C

`lamda=(log_(2)10)/(T)`

D

`lamda=(log_(2)e)/(T)`

Text Solution

Verified by Experts

The correct Answer is:
B
The relation between decay constant `lamda` and half-life T can be given as
`T=(0.693)/(lamda)`
`:.T=(log_(e))/(lamda)`
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Knowledge Check

  • Half life of a radioactive substance with progress of time

    A
    increase
    B
    decrease
    C
    remain same
    D
    none

  • The relationship between distintegration constant (lambda) and half-life (T) will be

    A
    `lambda=(log_(10) 2)/(T)`
    B
    `lambda=(log_(e)2)/(T)`
    C
    `lambda=(T)/(log_(e)2)`
    D
    `lambda=(log_(2)e)/(T)`

  • A radioactive isotope is being produced at a constant rate x. Half-life of the radioactive substance is y. After sometimes no. of radioactive nuclei becomes constant , the value of this constant is

    A
    `( xy )/( ln 2)`
    B
    xy
    C
    `( ln 2 ) xy `
    D
    `( x)/( y )`

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    Obtain the relation N=N_(0)e^(-lamdat) for a sample of radio active material having decay constant lamda where N is the number of nuclei present at instant t. Hence, obtain the relation between decay constant lamda and half life T_(1//2) of the sample.

    Write the relation between half-life and decay constant of a radioactive sample.

    Write the relation between average life and decay constant of a radioactive atom.

    Assertion Two different radioactive substances have initially same number of nuclei. Their decay constants are lamda_(1)and lamda_(2)(ltlamda_(1)). Then, initially first radioactiv substance decays at faster rate. Reason Half-life of first radioactive substance is less.

    The average life T and the decay constant lamda of a radioactive nucleus are related as

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