Question

Which fraction of an original 20.00-gram sample of nitrogen-16 remains unchanged after 35.65 seconds?

Answer 1

Approximately 1/32 grams of the original sample of 20.00 grams of nitrogen-16 would remain unchanged after 35.65 seconds

Answer 2

1/32 = 0.03125 = 3.125%

Step-by-step explanation:

The nitrogen-16 is an unstable isotope of nitrogen. The isotopes are the elements with the same atomic number but have a different number of mass. It means that they have a different number of neutrons (mass = protons + neutrons).

Because it is unstable, it decays in particles beta(β) and alpha (α), and the time that is necessary to the half of the mass disappear is called half-life which is equal to 7.13 s for nitrogen-16.

The mass that remains (m) can be calculated by:

m = m0/2ˣ, where m0 is the initial mass, and x the number of half-lives.

x = time/half-life time

x = 35.65/7.13

x = 5

Then,

m = 20.00/2⁵

m = 20.00/32

m = 0.625 g

The fraction is the mass that remains divided by the original mass:

0.625/20.00 = 1/32 = 0.03125 = 3.125%