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Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 10^{15}, calculate the energy of the source.

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#### Solution

Frequency of radiation (ν),

`"v" = 1/(2.0 xx 10^(9))`

`"v" = 5.0 xx 10^8 " s"^(-1)`

Energy (E) of source = Nhν

Where,

N = number of photons emitted

h = Planck’s constant

ν = frequency of radiation

Substituting the values in the given expression of (E):

E = (2.5 × 10^{15}) (6.626 × 10^{–34} Js) (5.0 × 10^{8} s^{–1})

E = 8.282 × 10^{–10} J

Hence, the energy of the source (E) is 8.282 × 10^{–10} J.

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