1108 SODIUM ATOMS AND 6108 POTASSIUM ATOMS ARE SIMULTANEOUSL

1*10^8 SODIUM ATOMS AND 6*10^8 POTASSIUM ATOMS ARE SIMULTANEOUSLY EXCITED TO THE 3P STATE AND 4P STATE, RESPECTIVELY. HOW MANY POTASSIUM ATOMS REAMIN IN THE 4P STATE WHEN 60% OF THE EXCITED SODIUM ATOMS HAVE DECAYED?

Solution

life time of the atoms in the excited state is approximately same for both the states

N = N₀exp(-t/T) where T is the life time of the atom the in the exited state

in the case of Na 60% decayed

N = 0.4 N₀   40% remianed in the excited state.

N/N₀ = 0.4   = exp(-t/T)

for Potasium atoms reamining the excited stated during the same time would be 0.4 or 40 %

6e8 *0.4 = 2.4e8 atomes remain in the 4P excited state.