## CHAPTER 07 REGULAR HOMEWORK

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**Question 1**

Gamma rays are electromagnetic radiation of very short wavelength emitted by the nuclei of radioactive elements. A certain radioactive element emits a gamma ray with a frequency of 1.51 x 1020 Hz. Express the wavelength of this radiation in picometers. (1Hz = 1 s-1 and 1 picometer = 1 x 10-12 m)

**Explanation**

**Explanation**

*λ*= c / f*c= 3E8 m/s* *λ = *(3E8 m/s)/ (1.51 E 20) = 1.987 E-12 = 1.987 pm

**Question 2**

The photoelectric effect for a certain alloy has a threshold frequency of 9.20 x 1014 Hz. For light of this frequency, find the energy of one mole of photons (in kJ). Hint given in feedback

**Explanation**

**Explanation**

E = h x f x (Avogadro number) / 1000 E = (6.63E-34 ) (9.20E14) (6.02E23 photons) / 1000 = 367

**Question 3**

Electrons are ejected from sodium metal by any light that has a wavelength shorter than 544 nm. What is the kinetic energy of an electron (in J) that is ejected from sodium by light with a wavelength of 471 nm?

**Explanation**

**Explanation**

E = (hc/ *λ) – ( hc/λ)*

*E =*[ (3E8 x 6.63E-34)/ (544 E-9) ] – [**(3E8 x 6.63E-34)/ (213 E-9) ]***5.68E-19*

**E =****Question 4**

The charge of an electron is -1.602 x 10-19 C. For the photoelectric effect, how many microamperes (1 A = 1 C/s) of electrical current are produced when a metal is bombarded by 6.60×1013 photons each second? Assume that each photon has sufficient energy to eject one electron. (Note currents are reported as positive values.) Hint given in feedback

**Explanation**

**Explanation**

E = (photon charge) *x *(number of photons) / (1E-6) E = (1.602 x 10 -19 C ) *x *( 6.60×10 13) / (1E 6) = 8.49 mA

**Question 5**

What is the wavelength (in nm) of the line in the spectrum of the hydrogen atom that arises from the transition of the electron from the orbital with n =7 to the orbital with n = 3? Note, the line corresponds to the energy of the photon that is emitted in the transition.

**Explanation**

**Explanation**

E = -2.18E-18 ( 1/9 -1/49) =1.977E-19 (6.63E-34)(3E8)/ 1.977E-19 = 1009

**Question 6**

Find the de Broglie wavelength (in nm) associated with an electron that is moving with a velocity of 4890 km/s. The electron rest mass is 9.11 x 10-31kg. Note, electrons having this speed would need to be treated as waves in atoms because the wavelength is on the order of the size of atoms.

**Explanation**

**Explanation**

λ = (6.63E-34)/ (4890E3)(9.11E-31) = .1487 nm

**Question 7**

A baseball weighs 220 g. Top speed for a professional pitcher is about 100 mph when he throws a fast ball. Find the de Broglie wavelength (in nm) associated with a baseball that is moving with a velocity of 45 mph. Hint given in feedback

**Explanation**

**Explanation**

λ = (6.63E-34)/ (.220kg)(20.1) = 1.499E-34 / 1E-9 = 1.5E-25 nm

**Question 8**

In each statement below, a set of quantum numbers is given. Check the allowed combinations of n, l, ml, and ms. (n = principle quantum number, l = angular momentum q.n., ml = magnetic q.n., and ms = electron spin q.n.) Select one or more:

**Explanation**

**Explanation**

**Question 9**

In each statement below, a set of quantum numbers is given. Match the 4d subshell with the correct allowed combinations of n, l, ml, and ms. Select one:

**Explanation**

**Explanation**

**Question 10**

In each statement below, a set of quantum numbers is given. Match the 2s subshell with the correct allowed combinations of n, l, ml, and ms. Select one:

**Explanation**

**Explanation**

**Question 11**

In each statement below, a set of quantum numbers is given. Match the 3d subshell with the correct allowed combinations of n, l, ml, and ms. Select one:

**Explanation**

**Explanation**

**Question 12**

For the orbital with n = 3, l = 0, which of the following is correct? Select one:

**Explanation**

**Explanation**

**Question 13**

For the orbital with n = 2, l = 1, which of the following is correct? Select one:

**Explanation**

**Explanation**

**Question 14**

For the orbital with n = 3, l = 2, which of the following is correct? Select one:

**Explanation**

**Explanation**

**Question 15**

For all elements with Z less than or equal to 10, check those that are diamagnetic. Hint given in feedback Select one or more:

**Explanation**

**Explanation**

**Question 16**

For all elements with Z less than or equal to 10, check the element with the greatest paramagnetism. Select one:

**Explanation**

**Explanation**

**Question 17**

For all elements with Z less than or equal to 10, check those that have one unpaired electron. Select one or more:

**Explanation**

**Explanation**

**Question 18**

Find the uncertainty in position (in nm) associated with an electron that is moving with a velocity of 452 km/s. The uncertainty in the velocity is 5.00%. The electron rest mass is 9.11 x 10-31 kg.

**Explanation**

**Explanation**

dx ≥ h / 4πmdu dx = uncertainty in position h = planck’s constant m = mass du = uncertainty in velocity du = 452E3 m/s * 0.05 = 22600 m/s dx ≥ (6.626E-34) / 4π * 9.11E-31 * 22600 ≥2.56E-9 2.56E-9 m = 2.56 nm

**Question 19**

The classical speed of an electron is similar to the speeds given in the previous problem. For example the classical speed of an electron in the ground state of a H atom is 220 km/s. The uncertainty in positions given in the last problem are on the order of the sizes of atoms. What does this suggest for electrons in atoms? Select one:

**Explanation**

**Explanation**

**Heisenberg’s uncertainty principle**: In other words, the more accurately we know the position of an electron , the less accurately we can know its velocity and vice versa.

**Question 20**

SKIP–NO POINTS. Find the uncertainty in position (in m) associated with a 650 kg automobile that is moving at 76 km/hr. The uncertainty in the velocity is 1%.

**Explanation**

**Explanation**

SKIP NO POINTS

**Question 21**

SKIP–NO POINTS. What does this answer imply for an automobile? Select one:

**Explanation**

**Explanation**

SKIP NO POINTS

**Question 22**

An electron in the 5th energy level of the H atom drops to the 3th energy level. In other words an electron in an excited state drops to a less excited state. What is the energy (in J) of the emitted photon? The energy of an electron in the nth level is En = – B

n2= – 2.18 x 10-18 J

n2

**Explanation**

**Explanation**

E = -2.18E-18 ( 1/9 -1/25) E = 1.55E-19

**Question 23**

SKIP–NO POINTS. An electron in the 6th energy level of the H atom drops to the 1st energy level. In other words an excited electron drops to the ground state. What is the energy (in J) of the emitted photon)? The energy of an electron in the nth level is En = – B

n2= – 2.18 x 10-18 J

n2

**Explanation**

**Explanation**

SKIP NO POINTS

**Question 24**

Simplified. The absorption spectra of ions have been used to identify the presence of the elements in the atmospheres of the sun and other stars. What is the energy of a photon (in J) that is absorbed by He+ ions, when an electron is excited from the Bohr orbit with n = 1 to the n = 3 state? The energy of an electron in the nth level is En = – *BZ*2

n2 where *B* = 2.18 x 10-18 J and *Z* = charge on nucleus (number of protons).

**Explanation**

**Explanation**

Ef = -2.18E-18 (22 / 3 2 ) = -9.688 E -19 E i= -2.18E-18 (22 / 1 2 ) = -8.72E-18 Ef – E i -9.688 E -19 – -8.72E-18 = 7.75E-18