Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 240 nm, what is the maximum possible velocity of the emitted electrons?

검증된 단계별 안내

Convert the wavelength of the light from nanometers to meters by using the conversion factor: 1 nm = 1 x 10^{-9} m.

Calculate the energy of the photons using the equation E = \(\frac{hc}{\lambda}\), where h is Planck's constant (6.626 x 10^{-34} J\(\cdot\) s), c is the speed of light (3.00 x 10^8 m/s), and \(\lambda\) is the wavelength in meters.

Determine the kinetic energy of the emitted electrons by subtracting the energy threshold from the photon energy: KE = E_{photon} - E_{threshold}.

Use the kinetic energy to find the maximum velocity of the emitted electrons with the equation KE = \(\frac{1}{2}\)mv^2, where m is the mass of an electron (9.11 x 10^{-31} kg).

Solve for the velocity v by rearranging the equation to v = \(\sqrt{\frac{2 \times KE}{m}\)}.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have energy greater than a material's work function to eject electrons. The energy of a photon is calculated using the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.

Energy of a Photon

The energy of a photon is directly related to its wavelength and can be calculated using the formula E = hc/λ. In this equation, h represents Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For the photoelectric effect to occur, the energy of the incoming photon must exceed the material's energy threshold, or work function.

Kinetic Energy of Emitted Electrons

When a photon with energy greater than the work function of a material ejects an electron, the excess energy is converted into the kinetic energy of the emitted electron. The kinetic energy (KE) can be calculated using the equation KE = E - φ, where E is the energy of the incoming photon and φ is the work function. This relationship allows us to determine the maximum velocity of the emitted electrons using the kinetic energy formula KE = 1/2 mv², where m is the mass of the electron.