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Question
Using de Broglie’s hypothesis, obtain the mathematical form of Bohr’s second postulate.
Solution
- De Broglie suggested that instead of considering the orbiting electrons inside atoms as particles, they should be viewed as standing waves. Also, the length of the orbit of an electron should be an integral multiple of its wavelength.
- Now, the distance travelled by an electron in one complete revolution in nth orbit of radius rn is 2πrn and it should be an integral multiple of the wavelength.
∴ 2πrn = nλ ....(1)
where, n = 1, 2, 3, 4…. - By de Broglie hypothesis,
`lambda = "h"/"p"_"n" = "h"/("m"_"e""v"_"n")` - Substituting this value of ‘λ’ in equation (1),
momentum of electron, pn = `"nh"/(2pi"r"_"n")`
∴ Angular momentum of electron Ln = pnrn = `"nh"/(2pi)`
Thus, the mathematical form of Bohr's second postulate is obtained.
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