Pls solve no 8 with detailed steps and explain the question pls dont give any - Chemistry - Chemical Kinetics

Question

Pls solve no 8 with detailed steps and explain the question pls
dont give any link as the answer
Q 8 An α -active radioisotope of He is kept in a sealed
container The mass of the radioisotope in the container is 5 g The
volume of He gas collected in 2 hours is 22 4 mL after
disintegration of the radioisotope What is the half life of the
radioisotope?
A 3120 3 years
B 3123 3 years
C 3460 3 years
D 3463 3 years

Vartika Jain · Accepted Answer

Dear Student,

As volume of He gas collected at STP = 22
4 ml22
4 L or 22400 ml of volume is occupied by 1 mol i
e  4 g of HeSo, 22
4 ml of volume will be occupied by 422400×22
4=0
004 g of HeAs initial amount of radioisotope , N0=5 g Amount of radioisotope disintegrated =0
004 gSo, amount of radioisotope that remains after 2hrN = 5-0
004=4
996 gt= 2hr 1 yr = 365 daysand, 1 day = 24 hrSo, 1 yr= 365×24 hrSo 1 hr=1365×24yrSo, 2 hr=2365×24yrAs logN0N=λt2
303so, λ=2
303tlog N0N        =2
3032365×24yrlog 5 4
996        =10087
14 ×0
00348 yr-1        =35
187 yr-1t12=0 693λ      =0
69335 187 yr-1      =0
0197 yr
There seems to be some problem in the options given