Question

1. a violet photon has a frequency of 7 100 × 10¹⁴ hz. (a) what is the wavelength (in nm) of the photon? (b) what is the energy of the photon?
2. the energy of a wave is measured at 4.6 × 10⁻¹⁹ j. what is the wavelength of the wave?
3. complete the following table

mass (g)	volume (ml)	density (g/ml)
	12.6	1.44
27.5		2.80

Explanation:

Problem 15

Step1: Relate wavelength to frequency

Use $c = \lambda
u$, rearrange to $\lambda = \frac{c}{
u}$.
$c = 3.00 \times 10^8 \, \text{m/s}$, $
u = 7.100 \times 10^{14} \, \text{Hz}$
$$\lambda = \frac{3.00 \times 10^8}{7.100 \times 10^{14}} = 4.225 \times 10^{-7} \, \text{m}$$

Step2: Convert meters to nanometers

$1 \, \text{m} = 10^9 \, \text{nm}$
$$\lambda = 4.225 \times 10^{-7} \times 10^9 = 422.5 \, \text{nm}$$

Step3: Calculate photon energy

Use $E = h
u$, $h = 6.626 \times 10^{-34} \, \text{J·s}$
$$E = 6.626 \times 10^{-34} \times 7.100 \times 10^{14} = 4.704 \times 10^{-19} \, \text{J}$$

Step1: Relate energy to wavelength

Use $E = \frac{hc}{\lambda}$, rearrange to $\lambda = \frac{hc}{E}$.
$h = 6.626 \times 10^{-34} \, \text{J·s}$, $c = 3.00 \times 10^8 \, \text{m/s}$, $E = 4.6 \times 10^{-19} \, \text{J}$
$$\lambda = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{4.6 \times 10^{-19}}$$

Step2: Compute and convert to nm

$$\lambda = 4.32 \times 10^{-7} \, \text{m} = 432 \, \text{nm}$$

Step1: Calculate density (row1)

Use $
ho = \frac{m}{V}$

$$ ho = \frac{54.3}{25.4} = 2.14 \, \text{g/mL}$$

Step2: Calculate mass (row2)

Use $m =
ho V$
$$m = 1.44 \times 12.6 = 18.1 \, \text{g}$$

Step3: Calculate volume (row3)

Use $V = \frac{m}{
ho}$
$$V = \frac{27.5}{2.80} = 9.82 \, \text{mL}$$

Answer:

(a) $422.5 \, \text{nm}$
(b) $4.704 \times 10^{-19} \, \text{J}$

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Problem 16