Question

Halflife of a radioactive substance a is two times the halflife of another radioactive substance b. Initially, the number of a and b are na and nb , respectively. After three halflives of a, number of nuclei of both are equal. Then, the ratio na /nb is

Answer 1

Hello miss,

● Answer -
na/nb = 1/8

● Explaination-
Let λa and λb be the the corresponding half lives.
Also na, nb be number of atoms before.

Let n'a be atoms after 3 half lives of a.
n'a = na / 2^3
n'a = na / 8

Let n'b be atoms after 3 half lives of a, i.e. 6 half lives of b.
n'b = nb / 2^6
n'b = nb / 64

Also we have,
n'a = n'b
na / 8 = nb / 64
na / nb = 1 / 8

Hope this is useful...