Question

For a radioactive material, half life is 20 days. If initially there are 800 gm of element, the time required for the disintegration of 600 gm of the element is:
1. 40 days
2. 20 days
3. 30 days
4. 60 days

Answer 1

Correct Answer - Option 1 : 40 days

CONCEPT:

Radioactivity: 

• Radioactivity is a process by which the nucleus of an unstable atom loses energy by emitting radiation.
  • ​Two forces, namely the force of repulsion that is electrostatic and the powerful forces of attraction of the nucleus acts in the nucleus.
  • These two forces are considered extremely strong in nature. The instability of the nucleus increases as the size of the nucleus increases because the mass of the nucleus becomes a lot to concentrate on.
  • That’s the reason why atoms of Plutonium, Uranium are extremely unstable and show radioactivity.

Half-life (t1/2):

• Half-life is the time period after which half of the quantity of the radioactive element gets decayed.

• It is given as,

\(⇒ T_{1/2}=\frac{0.693}{λ}\)

Where λ = decay constant

CALCULATION:

Given, t1/2 = 20 days, No = 800 gm and ΔN = 600 gm

• The quantity that remains after disintegration,

⇒ ΔN = N_o - N

⇒ N = No - ΔN

⇒ N = 800 - 600

⇒ N = 200

• We know that the substance remains after n half-life,

\(⇒ N=\frac{N_{o}}{2^{n}}\)     -----(1)

Where N = amount remaining after n half-life and No = initial amount

By equation 1,

\(⇒ 200=\frac{800}{2^{n}}\)

⇒ 2ⁿ = 4

⇒ 2n = 2²

⇒ n = 2 half life

• So the time required for the disintegration of 600 gm of the element is given as,

⇒ t = nt1/2

⇒ t = 2 × 20 days

⇒ t = 40 days

• Hence, option 1 is correct.