Question

Find the wavelength of the photon emitted when hydrogen makes a transition n = 10 ? 2.

Answer 1

Formula
1 / L = R ( ( 1 /nf ^2 ) - ( 1 / ni ^2 ) )

where (L) is your wavelength, (R) is the Rydberg constant, (ni) is your initial level and (nf) is your final level.


1 / L = 1.097 x 10 ^7 ( ( 1 /2^2 ) - ( 1 / 10 ^2 ) )
1 / L = 2632800
L = 3.798 x 10 ^ -7 metres

Answer 2

Relevant Formula. Derived by quantised the energy of an electron around an atom. (hydrogen only), long long derivation, but the formula is well enough known, i'm sure you don't need to derive it so i'll just give it to you. (for hydrogen only remember)

Formula
1 / L = R ( ( 1 /nf ^2 ) - ( 1 / ni ^2 ) )

Filling in values
1 / L = 1.097 x 10 ^7 ( ( 1 /1 ^2 ) - ( 1 / 2 ^2 ) )
1 / L = 1.097 x 10 ^7 ( 1 - 0.25 )
1 / L = 8227500
L = 1 / 8227500
L = 1.215 x 10 ^ -7 metres
L = 121.5 nanometres

where (L) is your wavelength, (R) is the Rydberg constant, (ni) is your initial level and (nf) is your final level.

just plug your values in and you should get
(d) 121.5 nanometres

Answer 3

Relevant Formula. Derived by quantised the energy of an electron around an atom. (hydrogen only), long long derivation, but the formula is well enough known, i'm sure you don't need to derive it so i'll just give it to you. (for hydrogen only remember)

Formula
1 / L = R ( ( 1 /nf ^2 ) - ( 1 / ni ^2 ) )

Filling in values
1 / L = 1.097 * 10 ^7* ( ( 1 /2 ^2 ) - ( 1 / 10^2 ) )
L = 1 / 8227500
L = 3.79823762e-7 m
L = 379.82 nanometres

where (L) is your wavelength, (R) is the Rydberg constant, (ni) is your initial level and (nf) is your final level.

Answer 4

E = -13.6(1/4 - 1/100) = -3.264 eV

Therefore energy of the radiation = 3.264 eV = 5.23 * 10^-19 J

E = hc/lambada = 6.62 * 10^-34 * 3 * 10⁸ / lambada

lambada = 6.62 * 10^-34 * 3 * 10⁸ / 5.23 * 10^-19 J = 3.8 * 10^-7 m

lambada =  3.8 * 10^-7 m = 380 nm

Answer 5