Question

Rubidium–87 decays by beta decay with a half-life of 4.9 × 1010 yr. How many 87Rb atoms are in a moon rock sample that has a rubidium decay rate of 3,500 disintegrations per hour?

Answer 1

`N=2.138* 10^(19)`Rubidium atoms

Step-by-step explanation:

Given:

The half life of Rubidium-87 =
`4.9* 10^(11) years`

Decay rate, A = 3500 Disintegration per hr

Now, converting the half life in hrs

Half life in hrs will be = 4.9×10¹¹ yrs × 360 days/ 1yrs × 24 hrs / 1 days

Half life in hrs = 4.23×10¹⁵ hrs

Now, We know that

Activity (A) = λ N

where, N = number of atoms.

also,

`\lambda=(0.693)/(t^(1)/(2))`

where,

`{t^(1)/(2)` = half life

therefore,

`\lambda=(0.693)/(4.23* 10^(15))`

= 1.64×10⁻¹⁶ hr⁻¹

now,

`N=(A)/(\lambda)`

substituting the values in the equation we have

`N=(3500)/(1.64* 10^(-16))`

`N=2.138* 10^(19)`Rubidium atoms