Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (b) What wavelength of radiation will provide a photon of this energy?

Verified step by step guidance

Identify the relationship between frequency and wavelength using the speed of light equation: c = \nu \lambda, where c is the speed of light (3.00 \times 10^8 \text{ m/s}), \nu is the frequency, and \lambda is the wavelength.

Rearrange the equation to solve for wavelength (\lambda): \lambda = \frac{c}{\nu}.

Substitute the given frequency (\nu = 1.09 \times 10^{15} \text{ s}^{-1}) into the equation.

Use the speed of light (c = 3.00 \times 10^8 \text{ m/s}) in the equation.

Calculate the wavelength (\lambda) in meters, and if needed, convert it to nanometers by multiplying by 10^9.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation. This effect demonstrates the particle nature of light, as photons must have sufficient energy to overcome the work function of the material to eject electrons. The minimum energy required to eject an electron corresponds to a specific frequency of incident light.

Energy-Frequency Relationship

The energy of a photon is directly proportional to its frequency, described by the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency. This relationship indicates that higher frequency radiation has more energy, which is crucial for understanding the conditions under which electrons can be ejected from a material.

Wavelength-Frequency Relationship

The wavelength and frequency of electromagnetic radiation are inversely related, expressed by the equation c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s), λ is the wavelength, and ν is the frequency. This relationship allows us to calculate the wavelength of radiation needed to provide a specific photon energy, which is essential for solving problems related to the photoelectric effect.

Recommended video:

Guided course

00:31

Frequency-Wavelength Relationship

Related Practice

Textbook Question

A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?

views

Textbook Question

A stellar object is emitting radiation at 3.55 mm. a. What type of electromagnetic spectrum is this radiation? b. If a detector is capturing 3.2×108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?

Textbook Question

Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (a) What is the minimum energy needed to eject an electron?

Textbook Question

Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s - 1 before it can eject an electron from its surface via the photoelectric effect. (c) If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?

Textbook Question

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

views