The half life of a radio isotope is 3h. The mass of the isotope at time t=0 is 160 gm. What is the mass of the isotope left after 15 h ?

Options

A. 2.5g
B. 5g
C. 7.5g
D. 10g

Answer

B

Explanation

Initial mass of the isotopes = 160 g
Half life T = 3h, Time of decay = 25h
`therefore` No. of half lives `(n) = t/T = 15/3 = 5`
Mass depends upon the number of radioactive atoms.
`therefore (N)/(N_0) = (1/2)^n = (1/2)^5 = 1/32`
`therefore (M)/(M_0) = 1/32 therefore (M)/(160) = 1/32 therefore M = 160/32 = 5`
`therefore` Mass left after 15h = 5 g