Question

The radioactive decay of thallium-206 to lead has a half-life of 4.20 min. Strarting with 5.10*10^22 atoms of thallium-206, calculate the number of such atoms left after 42.0 ,in. Enter your answer in scientific notation.

Answer 1

Frofm relation

N_t = N₀ x (1/2)ⁿ

where, N₀ is the initial quantity of the atom that will decay, N_t is the quantity that still remains and has not yet decayed after a time t and n = number of t_1⁄2 (half-life of the decaying atom).

given N₀ = 5.1 x 10²² atoms, t_1⁄2 = 4.2 min and t = 42 min and N_t = ?

Fist calculate the total  t_1⁄2 present in 42 min ie. n

n = t / t_1⁄2

n = 42 /4.2

n = 10

From equation,

N₀ = 5.1 x 10²² x (1/2)¹⁰

N₀ =  5.1 x 10²² /  1024

N₀ = 4.98 x 10¹⁹ atoms