The half life of $U^{238}$ when 1 gram of it emits $1.23 \times 10^4$ alpha particle per second is: (taking 1 year $=3.155 \times 10^7$ second)

$1.84 \times 10^8$ years $2.413 \times 10^9$ years $4.519 \times 10^9$ years $6.2 \times 10^7$ years

$4.519 \times 10^9$ years

The correct answer is Option (3) → $4.519 \times 10^9$ years