Answer:
1. b.) The wavelength gets shorter as the frequency increases
2. X-rays < Ultraviolet radiation < Visible light < Infrared radiation
3. 2 × 10⁵ J
Explanation:
1. Wavelength vs frequency
fλ= c
f = c/λ
Thus, frequency and wavelength are inversely proportional.
The wavelength increases (gets longer) as the frequency decreases.
2. Order of increasing wavelength
X-rays < Ultraviolet radiation < Visible light < Infrared radiation
3. Energy of green light
(a) Energy of 1 photon
λ = 5 × 10² nm = 5 × 10² × 10⁻⁹ m = 5 × 10⁻⁷ m
fλ = c
f = c/λ = (2.998 × 10⁸ m·s⁻¹)/(5 × 10⁻⁷ m) = 6 × 10¹⁴ s⁻¹
E = hf = 6.626 × 10⁻³⁴ J·s × 6 × 10¹⁴ s⁻¹ = 4 × 10⁻¹⁹ J
(b) Energy of 1.0 mol of photons
[tex]\text{Energy} = \text{1.0 mol photons} \times \dfrac{6.022 \times 10^{23}\text{ photons }}{\text{1 mol photons }} \times \dfrac{4 \times 10^{-19}\text{ J}}{\text{1 photon }} = \mathbf{2 \times 10^{5}} \textbf{ J}\\\\\text{The energy of 1.0 mol of photons of green light is $\large \boxed{\mathbf{2 \times 10^{5}}\textbf{ J}}$}[/tex]
Note: The answer can have only one significant figure because that is all you gave for the wavelength of the light.
