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

Answer:

$N=2.138\times 10^{19}$Rubidium atoms

Explanation:

Given:

The half life of Rubidium-87 = $4.9\times 10^{11} years$

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,

$\lambda=\frac{0.693}{t^\frac{1}{2}}$

where,  

${t^\frac{1}{2}$ = half life

therefore,

$\lambda=\frac{0.693}{4.23\times 10^{15}}$

= 1.64×10⁻¹⁶ hr⁻¹

now,

$N=\frac{A}{\lambda}$

substituting the values in the equation we have

$N=\frac{3500}{1.64\times 10^{-16}}$

$N=2.138\times 10^{19}$Rubidium atoms