Question

Options are: stays in n=2 state, jumps to n=3 state, jumps to n=4 state, jumps to n=5 state, jumps to n=6 state, or is ionized.

A hydrogen atom in the n=7 state decays to the n=4 state. What is the wavelength of the photon that the hydrogen atom emits? Use hc=1240 nm ev. 2161.76 nm While in the first excited state, a hydrogen atom is illuminated by various wavelengths of light. What happens to the hydrogen atom when illuminated by each wavelength? 410.3 nm? jumps to n=3 statex 415.3 nm? -pick one- 328.5 nm? -pick one- Note: For a transition between bound states (finite n) you need to match the correct wavelength to about 8 significant figures. For this problem, treat a transition as happening if the wavelength is within 1.0 nm.

Answer 1

(1) E Calculate the energy of n= 7 state. 13.6eV n? 13.6 eV 72 =-0.27755 eV Calculate the energy of n= 4 state. 13.6 eV 42 = -0.85 eV E = Write the expression to calculate the energy of the photon emitted by hydrogen atom. E = E,-E =-0.27755eV-(-0.85eV) = 0.57245 eV Write the expression to calculate the wavelength of the emitted photon. hc 2= E 1240 nm eV 0.57245 eV 2166.13 nm

(2) For the first excited state, n= 2. From Rydberg's equation, write the expression for the wavelength is of light. 1 2 n in 1 1 =R, 1 1 1 = nz 2R, 1 1 1 2 2 n n ARH For wavelength 1 = 410.3nm, 1 1 2 n2 (2) (410.3x109 m)(1.097x10’m-) 1 1 2 4 4.5 1 0.0278267 n n = 5.99 m 26 If a hydrogen atom illuminated with a light of wavelength 410.3 nm, then the state of hydrogen atom will jumps to n=6 state

For wavelength 2 = 415.3nm, 1 1 1 = n (2) (415.3x10-9 m)(1.097x10' m") 1 1 na 4 4.555841 1 = = 0.03050 n nž = 32.7852 n -5.73 Since, n, is not an integer, the hydrogen atom stays in first excited state because there is no such state in the hydrogen atom to jump to higher state with energy absorbed by illuminated light of wavelength 1 = 415.3nm . If a hydrogen atom illuminated with a light of wavelength 2 = 415.3nm , then the state of hydrogen atom will jumps to n=2 state or stay in n=2 state If the hydrogen atom illuminated with light of wavelength 328.5 nm, then the hydrogen atom will be ionized since the energy (3.8 eV) of the light of wavelength 328.5 nm is greater than ionization energy (3.4 eV) of hydrogen atom in first excited state. Hence, the hydrogen atom is ionized