Question

He+: Using Bohr’s model, give the expression for the energy levels in the He+ ion.

(a) What is the binding energy of this ion?

(b) Give the expression of line spectrum for this ion in terms of the Rydberg constant.

(c) What is the longest wavelength for the first four series of this line spectrum.

Answer 1

$E_n=-\frac{m_e e^4}{n^2 8h^2\varepsilon_0^2},$

a)

$E=(N_p m_p+N_n m_n-M)c^2=27.3~MeV,$

b)

$\frac{1}{\lambda}=RZ^2(\frac{1}{n^2}-\frac{1}{m^2}),$

c)

$\lambda=(RZ^2(\frac{1}{4^2}-\frac{1}{5^2}))^{-1}=10127~Å.$