Question

How do you find initial quantum number (ni) when given the values c=3.00 x 10^8 h=6.63 x 10^-34 nf=2 nm=656.2 and m=6.562x10^-7

For the values; Red light= 656.2nm , Green light= 486.1nm, Blue light 434.0nm, and violet light= 410.0

Answer 1

Wavelength, = 656.2 nm

Energy, E = hC/

E = 6.63 x 10^-34 x 3 x 10⁸/6.562x10^-7= 3.03 x 10^-19 J

E = Rh ((1/nf²)-(1/ni²))

3.03 x 10^-19 J = Rh ((1/2²)-(1/ni²)

Rh = 2.180 x 10^-18 J

3.03 x 10^-19 J = 2.180 x 10^-18 J (0.25- 1/ni²)

0.303 /2.180 = (0.25- 1/ni²)

0.139 = (0.25- 1/ni²)

0.139-0.25 = - 1/ni²

-0.111 = - 1/ni²

ni² = 1/0.111 = 9.00

ni = 9 = 3

2) Green light -

Wavelength, = 486.1 nm

Energy, E = hC/

E = 6.63 x 10^-34 x 3 x 10⁸/4.861x10^-7= 4.092 x 10^-19 J

E = Rh ((1/nf²)-(1/ni²))

4.092 x 10^-19 J = Rh ((1/2²)-(1/ni²)

Rh = 2.180 x 10^-18 J

4.092 x 10^-19 J = 2.180 x 10^-18 J (0.25- 1/ni²)

0.4092 /2.180 = (0.25- 1/ni²)

0.188 = (0.25- 1/ni²)

0.188-0.25 = - 1/ni²

-0.062 = - 1/ni²

ni² = 1/0.062 = 16

ni = 16 = 4

3) Blue light -

Wavelength, = 434 nm

Energy, E = hC/

E = 6.63 x 10^-34 x 3 x 10⁸/4.34 x10^-7= 4.583 x 10^-19 J

E = Rh ((1/nf²)-(1/ni²))

4.583 x 10^-19 J = Rh ((1/2²)-(1/ni²)

Rh = 2.180 x 10^-18 J

4.583 x 10^-19 J = 2.180 x 10^-18 J (0.25- 1/ni²)

0.4583 /2.180 = (0.25- 1/ni²)

0.210 = (0.25- 1/ni²)

0.210-0.25 = - 1/ni²

-0.04 = - 1/ni²

ni² = 1/0.04 = 25

ni = 25 = 5

d) Violet light

Wavelength, = 410 nm

Energy, E = hC/

E = 6.63 x 10^-34 x 3 x 10⁸/4.1 x10^-7= 4.851 x 10^-19 J

E = Rh ((1/nf²)-(1/ni²))

4.851 x 10^-19 J = Rh ((1/2²)-(1/ni²)

Rh = 2.180 x 10^-18 J

4.851 x 10^-19 J = 2.180 x 10^-18 J (0.25- 1/ni²)

0.4851 /2.180 = (0.25- 1/ni²)

0.2225 = (0.25- 1/ni²)

0.2225-0.25 = - 1/ni²

-0.0275 = - 1/ni²

ni² = 1/0.0275 = 36.4

ni = 36.4 = 6.0