Solveeit Logo
Login

Question

Question: 1 mg radium has \(2.68 \times 10^{18}\) atoms; its half life is 1620 years. How many radium atoms wi...

1 mg radium has 2.68×10182.68 \times 10^{18} atoms; its half life is 1620 years. How many radium atoms will disintegrate from 1 mg of pure radium in 3240 years?

A

2.01×1092.01 \times 10^{9}

B

2.01×10182.01 \times 10^{18}

C

1.01×1091.01 \times 10^{9}

D

1.01×10181.01 \times 10^{18}

Answer

2.01×10182.01 \times 10^{18}

Explanation

Solution

:n=tT1/2=32401620=2n = \frac{t}{T_{1/2}} = \frac{3240}{1620} = 2

As NN0=mm0=(12)n\frac{N}{N_{0}} = \frac{m}{m_{0}} = \left( \frac{1}{2} \right)^{n}

Mass of radium left after 2 half lives is

m=m0(12)n=1×(12)2=14=0.25mgm = m_{0}\left( \frac{1}{2} \right)^{n} = 1 \times \left( \frac{1}{2} \right)^{2} = \frac{1}{4} = 0.25mg

Mass of radium disintegrated=1−0.25=0.75mg= 1 - 0.25 = 0.75mg

Number of radium atoms disintegrated

=0.75×2.68×1018=2.01×1018= 0.75 \times 2.68 \times 10^{18} = 2.01 \times 10^{18}