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Chapter 1: Problem 19

If the wavelength of the light were to be shortened, how would that effect the kinetic energy of the ejected electron? (A) A shorter wavelength would increase the kinetic energy. (B) A shorter wavelength would decrease the kinetic energy. (C) A shorter wavelength would stop all electron emissions completely. (D) A shorter wavelength would have no effect on the kinetic energy of the ejected electrons.

Short Answer

Expert verified
A shorter wavelength would increase the kinetic energy (Option A)

Step by step solution

01

Understand the relationship between wavelength and frequency

The first thing to understand is the relationship between the light’s wavelength and its frequency. Planck's equation E = hν gives the energy of a photon, where E is energy, h is Planck's constant, and ν is frequency. Also, the frequency is related to the wavelength by the equation ν = c/λ, where c represents the speed of light and λ represents wavelength. Therefore, as the wavelength of light decreases, frequency ν increases.
02

Understand the Photoelectric effect

According to the photoelectric effect, the energy of an incident light photon is used to: 1) liberate an electron from the clutches of the atom and 2) account for the kinetic energy of the free electron. This can be represented as: hν = hν₀ + K.E, where h is Planck's constant, ν is the frequency of the incident light, ν0 is the threshold frequency and K.E is the kinetic energy of the electron. Since the frequency of the incident light is greater than the threshold frequency, we can see that any leftover energy from liberating the electron is given to the electron as kinetic energy. Since frequency increases (Step 1) when the wavelength decreases, K.E should also increase.
03

Determine the effect of shorter wavelength on the kinetic energy of the ejected electron

Finally, using the understanding of the relationship between wavelength and frequency of light, and the photoelectric effect, one can determine that a shorter wavelength of light, which translates to a higher frequency, imparts more energy to the electrons, liberating them and giving them more kinetic energy.

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Most popular questions from this chapter

A strong acid/strong base titration is completed using an indicator which changes color at the exact equivalence point of the titration. The protonated form of the indicator is HIn, and the deprotonated form is In. At the equivalence point of the reaction: (A) \([\mathrm{HIn}]=\left[\mathrm{In}^{-}\right]\) (B) \([\mathrm{HIn}]=1 /\left[\mathrm{In}^{-}\right]\) (C) \([\mathrm{HIn}]=2\left[\mathrm{In}^{-}\right]\) (D) \([\mathrm{HIn}]=\left[\mathrm{In}^{-}\right]^{2}\)

\(\mathrm{Cu}^{2+}+2 e^{-} \rightarrow \mathrm{Cu} \quad E^{\circ}=+0.3 \mathrm{V}\) \(\mathrm{Fe}^{2+}+2 e^{-} \rightarrow \mathrm{Fe} \quad E^{\circ}=-0.4 \mathrm{V}\) Based on the reduction potentials given above, what is the reaction potential for the following reaction? \(\mathrm{Fe}^{2+}+\mathrm{Cu} \rightarrow \mathrm{Fe}+\mathrm{Cu}^{2+}\) (A) \(-0.7 \mathrm{V}\) (B) \(-0.1 \mathrm{V}\) (C) \(+0.1 \mathrm{V}\) (D) \(+0.7 \mathrm{V}\)

In which of the following reactions is entropy increasing? (A) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) (B) \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\) (C) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) (D) \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

When calcium chloride \(\left(\mathrm{CaCl}_{2}\right)\) dissolves in water, the temperature of the water increases dramatically. Compared to \(\mathrm{CaCl}_{2},\) what must be true regarding the hydration energy of \(\mathrm{CaF}_{2} ?\) (A) It would be greater because fluoride is smaller than chloride. (B) It would be the same because the charges of fluoride and chloride are identical. (C) It would be the same because hydration energy is only dependent on the IMFs present in water. (D) It would be smaller because the molar mass of \(\mathrm{CaF}_{2}\) is smaller than that of \(\mathrm{CaCl}_{2}\) .

Questions 45-48 refer to the following. Inside a calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) hydrocyanic acid (HCN), a weak acid, and 100.0 \(\mathrm{mL}\) of 0.50 \(\mathrm{M}\) sodium hydroxide are mixed. The temperature of the mixture rises from \(21.5^{\circ} \mathrm{C}\) to \(28.5^{\circ} \mathrm{C}\) . The specific heat of the mixture is approximately \(4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C},\) and the density is identical to that of water. What is the approximate amount of heat released during the reaction? \(\begin{array}{ll}{\text { (A) }} & {1.5 \mathrm{kJ}} \\ {\text { (B) }} & {2.9 \mathrm{kJ}} \\ {\text { (C) }} & {5.9 \mathrm{kJ}} \\ {\text { (D) }} & {11.8 \mathrm{kJ}}\end{array}\)
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