Calculation of wavelength of electron in ground state:
Radius of ground state of hydrogen atom =
0.53A˚=0.53×10−10mAccording to de Broglie relation
2πr=nλFor ground state
n=1 2×3.14×0.53×10−10=1×λ ∴λ=3.32×10−10m =3.32A˚AlternativelyVelocity of electron, in the ground state, of hydrogen atom
=2.18×10−6m/sHence momentum of revolving electron
p=mv =9.1×10−31×2.18 ×10−6kgm/s λ=ph =9.1×10−31×2.18×1066.63×10−34m =3.32A˚ [
Note : Also accept the following answer:
Let
λn be the wavelength of the electron in the
nth orbit, we then have
2πrn=nλ For ground state
n=1 2πrn=λ (
r=r0 is the radius of the ground state)
[Alternatively
λn=mvnhand
vn=v0 (velocity of electron in ground state)
λ=mvnh