Question

Cesium-137 has a half-life of 30.2 years. How many years will it take for a 100.0-g sample to decay to 0.01g?​

Answer 1

Answer:

Hello sir,

Ill be explaining ur question

Explanation:

Find the mass that remains after t years?

t = 30

Po=100

The equation for decay is Poekt

How do I find the relative growth rate?

So after realizing that the half the amount of 100mg would be 50mg I placed the 50 mg in my formula as the result. Thus,

50mg=100ek30

I divided both sides by 100:

50100=100ek30100

ln 0.5=ln ek30

ln 0.530=k

k= -0.023

Please mark me as the brillianist ;)

Answer 2

Given: Cesium-137 has a half-life of 30.2 years.

To find: Time taken for a 100 g sample to decay to 0.01 g

Explanation: Half life of the reaction= 30.2 years

Rate constant of the reaction

= ln 2 / half life

= 0.69/ 30.2

Mass of sample before reaction= 100 g

Let time taken in years be t.

Mass of sample after time t= 1 g

The formula for calculating time for the reaction is given by the formula:

=>$t = \frac{2.3 \times log( \frac{100}{1} ) }{rate \: constant}$

=>$t = \frac{2.3 \times 2}{ \frac{0.69}{30.2} }$ ( log 100=2)

=>$t = \frac{2.3 \times 2 \times 30.2}{0.69}$

=>t = 201.33 years

Therefore, it takes 201.33 years for a 100 g sample to decay to 1 g sample.