Question

1. Given that a freshly prepared radioactive isotope has a half-life of 10 days, the percentage of it remaining after 30 days is

A	30.0 %.
B	10.0 %.
C	12.5 %.
D	72.5 %.

2. During a second half-life, the original material has decayed

A	25%.
B	50%.
C	75%.
D	100%.

Answer 1

1. Answer is C = 12.5%

Since half life period of the isotope is 10 days.

Then After first 10 days, 50% will be decay. then reamining amount is 50% of initial amount.

Then after another 10 days, 50% of remaining isotpe will decay. hence net 25% of initial amount will present.

Then After another 10 days,50% of remaining isotpe will decay. hence net 12.5% of initial amount will present .

Hence 12.5% of initial amount will reamin after 30 days.

2. Answer is C = 75%.

After first half life, 50 % will decay.

After second half-life 50% of remaing isotpe will decay. Hence 25% of initial amount will present. hence 75% of initial amount will decay.

Amount of isotopes present after n consucetive half-life is given by the equation

Where N = amount of isotpes present

N₀ = Initial amount of isotpe