The luminous dials of watches are usually made by mixing a zinc sulphide phosphor with an `alpha`-particles emitter. The mass of radium (mass number `226,half-life 1620 years`)that is needed to produce an average of `10` alpha`-particles per second for this purpose is

Options

A. `2.77 mg`
B. `2.77 g`
C. `2.77 xx10^(-23)g`
D. `2.77 xx10^(-13)kg`

Answer

d

Explanation

`|(dN)/(dt)|=lambdaN`
number of radium nuceli in `m g =(N_(A)m)/(226)`
Decay constant, `lambda =(0.693)/(t_(1//2)) =(0.693)/(1620 xx 3.16 xx10^(7))`
`|(dN)/(dt)|=10=(0.693 xx 10^(23)m)/(226) xx (0.693)/(1620 xx 3.16 xx10^(7))`
`:. m=(10 xx 226xx1620 xx 3.16 xx10^(7))/(6.02 xx 10^(23) xx0.693)`
`=2.77 xx 10^(-10) g`
`=2.77 xx 10^(-13) kg`.