Question

2.) Calculate the wavelength of the light emitted by hydrogen if an electron jumps from the n 6 to n-2 level. 3.) Calculate the radius of the n 4 level and the energy of this level according to the Bohr model.

2. Calculate the wavelength of the light emitted by hydrogen if an electron jumps from the n=6 to n=2 level

3. Calculate the radius of the n=4 level and the energy of this level according to the Bohr model

Thank you in advance!

Answer 1

The electron makes a transition from n = 6 to n = 2. We are dealing with a photon emission, which means that the energy difference(DE) is actually negative. DE = -R_4(1/n_f-1/n_i) where n_f = the final energy level n_i = the initial energy level R_H = 2.18*10^-18J -Rydberge constant expressed in J delta E = -2.18 times 10^-18(1/2^2-1/6^2) = -2.18 times 10^-18(0.222) = -4.84 times 10^-19J We know that the DE is equal to the energy of emitted photon which is always +ve. DE = -h nu-hc/ lambda \r\n lambda = hc/-DE h = Planck's constant c = speed of light c = 3.0 times 10^+8 J = 3.0 times 10^8J lambda = 6.626 times 10^-34*3.00 times 10^8(m/sec)/-(-4.84 times 10^-19)(J) lambda = 4.1070*10^-7m Since we're in the visible range of EM spectrum (400-700n) lambda = 4.1070 times 10^-7m = 410.70 times 10^-9m lambda = 410.70nm