Write a single equation that includes the following sets of variables: wavelengt

Question

Write a single equation that includes the following sets of variables: wavelength and frequency frequency and energy energy and wavelength Calculate the energy (In J) of a photon... with a frequency of 4.2*10^10 Hz with a wavelength of 38 cm What is the wavelength (in nm) of a photon with an energy of 9.72*10^-19 J Calculate the change in energy when an electron moves from the n=3 to n=1 level in a hydrogen atom Repeat question #4, but this time consider an electron in a He^* ion The energy is question #5 is greater than the energy in question #4 by a factor of A hydrogen atom in its ground state absorbs light with a wavelength of 102.6 nm. To which excited state would the electron be excited (i.e. identify n_t)

Explanation / Answer

1.

a.       c = ....where, c=velocity of light, = frequency of light, =wavelength of light

b.       E = h...where,E = energy, h= Plank's constant

c.       E = hc/

2.

a. E = h = (6.626*10-34 J.s ) * ( 4.2*1010 s-1) = 2.78*10-23 J

b. E= hc/ = (6.626*10-34 J.s ) * (3*108 m.s-1)/(0.38 m) = 5.23*10-25 J

3.

= hc/E = (6.626*10-34 J.s ) * (3*108 m.s-1)/(9.72*10-19 J)

= 2.04*10-7 m

= 204.5 nm

4.

= 1/ = Rz[(1/n1)2 - (1/n2)2 ] = (1.09768*107 m-1) [(1/1)2 - (1/3)2 ]

= 1.025*10-7 m

E = hc/ = (6.626*10-34 J.s ) * (3*108 m.s-1)/( 1.025*10-7 m) = 1.9*10-18 J

5. For He+, z = 2

Rz = z2.e4.m/82.ch3 = 1.09768*107 m-1 (for z=1)

for, He+, Rz = 4* 1.09768*107 m-1

for this case,

= 2.5625*10-8 m

E = hc/ = (6.626*10-34 J.s ) * (3*108 m.s-1)/( 2.5625*10-8 m) = 7.757*10-18 J

6. greater by factor = (7.757*10-18)/( 1.9*10-18) = 4

7.

= 102.6 nm = 102.6*10-9 m

= 1/ = 9746588.69 m-1 = Rz[(1/n1)2 - (1/n2)2 ] = (1.09768*107 m-1) [(1/1)2 - (1/n)2 ]

1- 1/n2 = 0.888

or, n = 3

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