Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant.
λ (nm) 500 450 400
v × 10–5 (cm s–1) 2.55 4.35 5.35
Let us suppose threshold wavelength to be λ nm the kinetic energy of the radiation is given as:
h (v-vo) = 1/2 mv2
Or
hc (1/λ -1/λo) = 1/2 mv2
……………………………. [1]
Similarly, we can also write,
……………………………………. [2]
………………………………………. [3]
Dividing equation [3] and [1]
17.6070λ - 5λ = 8803.537 – 2000
λ = [6805.537] / [12.607]
λ = 539.8 nm
The wavelength is 540 nm.
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