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Light Problem Set

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1. (a) What are the wavelength and color of the line in the Balmer spectrum for n2=4?
(b) What are the wavelength and color of the line for n2=5?

a. a) 486.08 nm and blue b) 434.00 nm and violet
b. a) 686.08 nm and red b) 634.00 nm and red
c. a) 386.08 nm and ultra violet b) 334.00 nm and ultra violet
d. a) 586.08 nm and orange b) 534.00 nm and green

2. The peak intensity of the solar spectrum occurs for lamda(max)= 475 nm. What is the temperature of the surface of the sun?

a. 5000 K
b. 6110 K
c. 4211 K
d. 8324 K

3. What is the wavelength of a quantum of light whose energy is 3.50 x 10^-19 J?

a. 658 nm
b. 635 nm
c. 568 nm
d. 865 nm

4. What is the minimum voltage required in an x-ray tube to produce photons whose wavelength is 0.10 nm?

a. 4.12 kV
b. 12.4 kV
c. 65.2 kV
d. 0.124 kV

5. A material has a photoelectric work function of 3.66 eV. What is the maximum speed of photoelectrons ejected from it by light of wavelength 250nm?

a. 677,000 m/s
b. 8200 m/s
c. 8654 m/s
d. 67700 m/s

6. Calculate the second Bohr radius of the hydrogen atom - that is the radius of n=2.

a. 21.2 nm
b. 2.12 nm
c. 0.212 nm
d. 243 nm

7. What is the longest-wavelength photon that can ionize a neutral hydrogen atom initially in the ground, or lowest, enegry state?

a. 91.2 nm
b. 9.12 nm
c. 70.1 nm
d. 52.1 nm

8. The spectral series corresponding to n1= 4 in hydrogen is called the Brackett series in honor of its discoverer. What are the longest and shortest wavelengths in the Brackett series?

a. 4.05 mcm and 1.46 mcm
b. 24.3 mcm and 8.6 mcm
c. 23.1 mcm and 12.5 mcm
d. 54.2 mcm and 32.1 mcm

Solution Summary

Formula and calculations are included for each question.

Solution Preview

1. For balmer series,

1/lambda = R(1/2^2 - 1/n^2)
a) n2 = 4
1/lambda = R(1/4 - 1/16)
==> 1/lambda = R(1/4 - 1/16)
==> lambda = 486.17nm.. which is blue.

2. TWe have the Weins Law:

lambda(max) = 2897 micrometer / T(K)
here, lanbda(max) = 475nm

==> T = 2897*10^-6/475*10^-9
==T = 6098.95 K

3. We have Energy = plancks constant * frequency

E = h*f
but, c= f*lambda, ==> f = c/lambda

==> E = h*c/lambda
==> E = 6.6*10^-34*3*10^8/lambda
==> lambda = ...

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