Q: What is the energy of a mole of photons with a wavelength of 242.4 nm? (Avogadro’s number $$N_A = 6.022 \times 10$$^{23}$$ mol$$^{-1}$$)

$$4.936 \times 10$$^{5}$$ J/mol

Question 1

A sodium vapor lamp emits light with a wavelength of 589 nm. What is the frequency of this radiation? (Speed of light $$c = 2.998 	imes 10^8$ m/s)

Accepted Answer

$$5.09 	imes 10$$^{14}$$ Hz

Question 2

Using Planck’s equation, what is the energy of a single photon with a wavelength of 242.4 nm? (Planck’s constant $$h = 6.626 	imes 10$$^{-34}$$ J·s, c = 2.998$$ 	imes $$10^8 m/s)$$

Accepted Answer

$$8.196 	imes 10$$^{-19}$$ J

Question 3

What is the energy of a mole of photons with a wavelength of 242.4 nm? (Avogadro’s number $$N_A = 6.022 	imes 10$$^{23}$$ mol$$^{-1}$$)

Accepted Answer

$$4.936 	imes 10$$^{5}$$ J/mol

Question 4

Is there an energy level for the hydrogen atom with $$E = -1.00 	imes 10$$^{-20}$$ J? (Rydberg constant R_H = 2.179$$ 	imes $$10^{-18} J)$$

Accepted Answer

No, because the calculated principal quantum number $$n is $$not an integer.

Question 5

Calculate the wavelength of the Balmer series line for hydrogen corresponding to the transition from $$n = 5 to$$ $$n = 2$$. ($$R_H = 2.179 	imes 10$$^{-18}$$ J, h = 6.626$$ 	imes $$10^{-34} J$$·s, $$c = 2.998 	imes 10^8$ m/s)

Accepted Answer

$$434.1 nm$$

Question 6

An electron is ionized from a Li$$^{2+}$$ ion in its ground state using a photon of frequency $$5.000 	imes 10$$^{16}$$ s$$^{-1}$$. What is the kinetic energy of the electron? (Z = 3$, R_H = 2.179$$ 	imes $$10^{-18} J$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s)

Accepted Answer

$$1.352 	imes 10$$^{-18}$$ J

Question 7

What is the wavelength associated with electrons traveling at one-tenth the speed of light? (Mass of electron $$m = 9.11 	imes 10$$^{-31}$$ kg, h = 6.626$$ 	imes $$10^{-34} J$$·s, $$v = 3.00 	imes 10^7$ m/s)

Accepted Answer

$$2.42 pm$$

Question 8

A 12 eV electron has a speed of $$2.05 	imes 10^6$ m/s. If the uncertainty in speed is 1.5%, what is the minimum uncertainty in position? (m = 9.11$$ 	imes $$10^{-31} kg$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s, $$\pi = 3.14$$)

Accepted Answer

About 10 atomic diameters

Question 9

For an electron in a one-dimensional box of length $$1.00 	imes 10^2$ pm, what is the energy difference between the ground state and the first excited state? (m = 9.11$$ 	imes $$10^{-31} kg$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s)

Accepted Answer

$$1.81 	imes 10$$^{-17}$$ J

Question 10

What is the wavelength of the photon that could excite an electron from the ground state to the first excited state in a one-dimensional box of length $$1.00 	imes 10^2$ pm? (h = 6.626$$ 	imes $$10^{-34} J$$·s, $$c = 3.00 	imes 10^8$ m/s, $$\Delta E = 1.81 	imes $$10^{-17} J)$$

Accepted Answer

$$11.0 nm$$

Question 11

Which equation correctly relates the energy of a photon to its frequency?

Accepted Answer

$$E = h
u$$

Question 12

Which equation is used to calculate the allowed energy levels of a hydrogen atom?

Accepted Answer

$$E_n = -\frac{R_H}{n^2$}$$

Question 13

Which equation is used to calculate the wavelength associated with a moving particle (de Broglie wavelength)?

Accepted Answer

$$\lambda = \frac{h}{mv}$$

Question 14

Which equation expresses the Heisenberg uncertainty principle for position and momentum?

Accepted Answer

$$\Delta x \Delta p \geq \frac{h}{4\pi}$$

Question 15

Which of the following best describes the quantization of energy in the hydrogen atom?

Accepted Answer

Only certain discrete energy levels are allowed, determined by integer values of $$n$$

Question 16

Which transition in the hydrogen atom would emit the highest energy photon?

Accepted Answer

From $$n = 2 to$$ $$n = 1$$

Question 17

Which of the following statements about the particle in a box model is correct?

Accepted Answer

The energy levels are proportional to $$n^2$$

Question 18

If the wavelength of light is decreased, what happens to the energy of its photons?

Accepted Answer

The energy increases

Question 19

Which real-world scenario best illustrates the application of the Heisenberg uncertainty principle?

Accepted Answer

Measuring the position and speed of an electron in an atom

Quantum Chemistry Practice Guidance – CHEM 1042

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