Question

A hydrogen atom is in its first excited state

(n = 2).

Using Bohr's atomic model, calculate the following.

(a)

the radius of the electron's orbit (in nm)

nm

(b)

the potential energy (in eV) of the electron

eV

(c)

the total energy (in eV) of the electron

eV

Answer 1

the radius of the electron's orbit is

r_n = n^2 r

= 2^2( 0.0529 nm)

=0.2116 nm

(b)

pE=- k e^2/ r= 9* 10^9 ( 1.6 * 10^-19)^2/ 0.2116 * 10^-9

=-1.09*10^-18/(1.6*10^-19)

= -6.8 eV

(c)

balance with centripetal force with electric force

m_evn²/r_n =ke²/r_n²

_vn=sqrtke²/m_er_n

_v2=sqrt(9*10⁹)(1.6*10^-19)²/(9.11*10^-31)(0.2116*10^-9)

_v2=1.09*10⁶ m/s

kinetic energy( kE) = 1/2 m v2^2= 1/2* ( 9.11 * 10^-31) ( 1.09* 10^6)^2 = (5.44*10^-19)/(1.6*10^-19) =3.4 eV

(c)

E = pE + kE = 3.4 eV-6.8 eV = -3.4 eV