Question

Ch 29

44. In an atom, an electron has the following allowed energy levels, E1 = 1 eV, E2 = 4 eV and E3 = 6 eV. What are the observed emission and absorption wavelengths for this atom? Absorption: 414.4 nm, 248.6 nm, Emission: 414.4 nm, 248.6 nm, 621.6 nm

45. In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short pulses of light, each containing 1 mJ of energy. a) In each pulse there are 9.7 x 1014 photons. What is the wavelength of the laser? 192.9 nm b) Each pulse lasts only 20 nsec. What is the average power delivered to the eye during a pulse? 50kW

46. An electron with a speed of 4 x 106 m/s collides with an atom. The collision excites the atom from its ground state (1 eV) to a state with an energy of 8.9 eV. What is the speed of the electron after the collision? 3.64 x 106 m/s

48. The absorption spectrum for an atom consists of the wavelengths 200 nm, 300 nm and 500 nm.

a) Draw the energy level diagram for this atom, labeling the energy (in eV) for each level. The ground state energy level is at 0 eV. E2 = 2.49 eV. E3 = 4.14 eV, E4 = 6.22 eV

b) What wavelengths are seen in the emission spectrum? 753.4 nm, 333.3 nm, 597.7 nm

Answer 1

44. E₁=1 eV, E₂=4eV, E₃=6eV

We know that E=hc/, where E is energy, h is planck's constant with value 6.626*10^-34J-s ,c is speed of light=3*10⁸ m/s, is wavelength of emitted electromagnetic wave.

for state 1 to state 2 transition:

change in energy=E₂-E₁=4-1=3 eV=3*1.6*10^-19 J= 4.8*10^-19 J

therefore, hc/=4.8*10^-19 =>6.626*10^-34*3*10⁸/=4.8*10^-19

=>=6.626*10^-34*3*10⁸/(4.8*10^-19)=4.14*10^-7 m=414*10^-9 m=414 nm

Since, this is a transition from lower energy state to higher energy state,this will be achieved with absorption of wavelength 414 nm.

for state 2 to state 3 transition:

change in energy=E₃-E₂=6-4=2 eV=2*1.6*10^-19 J= 3.2*10^-19 J

therefore, hc/=3.2*10^-19 =>6.626*10^-34*3*10⁸/=3.2*10^-19

=>=6.626*10^-34*3*10⁸/(3.2*10^-19)=6.21*10^-7 m=621*10^-9 m=621 nm

Since, this is a transition from lower energy state to higher energy state,this will be achieved with absorption of wavelength 621 nm.

for state 1 to state 3 transition:

change in energy=E₃-E₁=6-1=5 eV=5*1.6*10^-19 J= 8*10^-19 J

therefore, hc/=8*10^-19 =>6.626*10^-34*3*10⁸/=8*10^-19

=>=6.626*10^-34*3*10⁸/(8*10^-19)=2.48*10^-7 m=248*10^-9 m=248 nm

Since, this is a transition from lower energy state to higher energy state,this will be achieved with absorption of wavelength 621 nm.

for state 2 to state 1 transition:

magnitude of change in energy=E₂-E₁=4-1=3 eV=3*1.6*10^-19 J= 4.8*10^-19 J

therefore, hc/=4.8*10^-19 =>6.626*10^-34*3*10⁸/=4.8*10^-19

=>=6.626*10^-34*3*10⁸/(4.8*10^-19)=4.14*10^-7 m=414*10^-9 m=414 nm

Since, this is a transition from higher energy state to lower energy state,this will be achieved with emission of wavelength 414 nm.

for state 3 to state 2 transition:

magnitude of change in energy=E₃-E₂=6-4=2 eV=2*1.6*10^-19 J= 3.2*10^-19 J

therefore, hc/=3.2*10^-19 =>6.626*10^-34*3*10⁸/=3.2*10^-19

=>=6.626*10^-34*3*10⁸/(3.2*10^-19)=6.21*10^-7 m=621*10^-9 m=621 nm

Since, this is a transition from higher energy state to lower energy state,this will be achieved with emission of wavelength 621 nm.

for state 3 to state 1 transition:

magnitude of change in energy=E₃-E₁=6-1=5 eV=5*1.6*10^-19 J= 8*10^-19 J

therefore, hc/=8*10^-19 =>6.626*10^-34*3*10⁸/=8*10^-19

=>=6.626*10^-34*3*10⁸/(8*10^-19)=2.48*10^-7 m=248*10^-9 m=248 nm

Since, this is a transition from higher energy state to lower energy state,this will be achieved with emission of wavelength 621 nm.