Topic 5.2: Quantum physics (HL) Questions

Light is shone on a metal above its threshold frequency, ejecting electrons. The frequency of the light is then DOUBLED while the intensity is kept the same. What happens to the maximum kinetic energy of the ejected electrons?

A photon of light has frequency 4.0 × 10¹⁴ Hz. What is its energy? (h = 6.63 × 10⁻³⁴ J s.)

The kinetic energy of a free electron is increased by a factor of 9. By what factor does its de Broglie wavelength change?

A proton is accelerated from rest through a potential difference of 200 V. Its de Broglie wavelength is closest to: (m_p = 1.67 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C, h = 6.63 × 10⁻³⁴ J s)

A metal has a work function of 4.0 × 10⁻¹⁹ J. What is its threshold frequency — the lowest frequency of light that will eject electrons? (h = 6.63 × 10⁻³⁴ J s.)

Ultraviolet light ejects electrons from a metal with maximum kinetic energy 1.6 × 10⁻¹⁹ J. What stopping voltage just reduces the photocurrent to zero? (e = 1.60 × 10⁻¹⁹ C.)

Which expression gives the de Broglie wavelength λ of a particle of mass m moving with kinetic energy K?

The kinetic energy of a particle is increased to four times its original value. By what factor does its de Broglie wavelength change? (λ = h/√(2mE_k).)

An electron is accelerated until it has a momentum of 4.0 × 10⁻²⁴ kg m s⁻¹. (a) Determine its de Broglie wavelength. (b) Explain why a beam of these electrons can be diffracted by a crystal but a beam of tennis balls cannot.

The position of an electron is measured to within an uncertainty of Δx = 2.0 × 10⁻¹⁰ m. Determine the minimum uncertainty in its momentum.

A student claims that making a beam of light brighter will always eject electrons from any metal. Explain, using the photon model, why this is wrong.

In a photoelectric experiment, light of frequency 7.5 × 10¹⁴ Hz is shone on a metal surface whose work function is 3.0 × 10⁻¹⁹ J. (a) Calculate the energy of one photon. (b) Determine the maximum kinetic energy of an ejected electron.

A beam of neutrons (mass 1.67 × 10⁻²⁷ kg) moving at 3.0 × 10³ m s⁻¹ is directed at a crystal and produces a diffraction pattern.

(a) Calculate the de Broglie wavelength of the neutrons.
(b) Explain why a diffraction pattern is observed for these neutrons but not for a beam of fast tennis balls.

A proton and an electron move with the same speed.

(a) State which has the longer de Broglie wavelength.
(b) The proton mass is 1836 times the electron mass. Determine the ratio (de Broglie wavelength of the proton) / (de Broglie wavelength of the electron).

The longest wavelength of light that will eject electrons from a clean metal surface (the threshold wavelength) is measured to be 5.4 × 10⁻⁷ m. Show that the work function of the metal is about 2.3 eV. (1 eV = 1.60 × 10⁻¹⁹ J.)

A laser emits monochromatic light of frequency 5.0 × 10¹⁴ Hz with an output power of 2.4 mW. (a) Determine the energy of one photon. (b) Calculate the number of photons the laser emits each second.

A free electron has a kinetic energy of 5.0 × 10⁻¹⁸ J.

Determine its de Broglie wavelength. (mass of electron = 9.11 × 10⁻³¹ kg)

The position of an electron is known to within Δx = 1.0 × 10⁻⁹ m. What is the minimum uncertainty in its momentum? (h = 6.63 × 10⁻³⁴ J s)

An electron has a kinetic energy of 2.5 × 10⁻¹⁷ J. What is its de Broglie wavelength? (m_e = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s)

Outline the evidence that light behaves as a particle.