Physics Chapter on Quantum Concepts

What is the ratio of the de-Broglie wavelength associated with an electron and the wavelength of a photon with the same energy E?

If a beam of electromagnetic radiation of intensity 6.4 × 10–5 W/cm² with wavelength 310 nm ejects 10^x electrons in 1s, what is x?

What is the frequency of revolution of the electron in its first excited state in a hydrogen atom if the time period of revolution in its ground state is 1.6 × 10–16 s?

If a photon of energy 4.0 eV strikes a metal and the maximum kinetic energy of the ejected photoelectrons is TA eV, what is the maximum kinetic energy when another photon of energy 4.50 eV strikes a different metal?

If the de-Broglie wavelength of photoelectrons from metal B is twice that of metal A, what is the work function of metal B if photon energy is 4.0 eV in metal A?

What is the wavelength of the second member of the Balmer series in nm if the first member of the series has a wavelength of 6561 Å?

De Broglie Wavelength

The ratio of the de Broglie wavelength of an electron and the wavelength of a photon with the same energy (E) is given by:
- c(2mE)^1/2
- Where:
  - c is the speed of light
  - m is the mass of the electron
  - E is the energy

Photoelectric Effect

A beam of electromagnetic radiation with a wavelength of 310 nm and intensity of 6.4 × 10-5 W/cm2 falls on a metal surface.
The metal has a work function of 2 eV.
Every 103 photons eject one electron.
The number of electrons ejected per second is 10x.

Atomic Spectra and Energy Levels

The hydrogen atom has energy levels corresponding to different electron orbits.
Transitions between these levels result in the emission or absorption of photons.
The Balmer series corresponds to transitions to the n = 2 level.
The first member of the Balmer series has a wavelength of 6561 Å.
The wavelength of the second member of the Balmer series is 486.1 nm.

Electron in an Electric Field

An electron with initial velocity v0iˆ + v0 ˆj is placed in an electric field −E0kˆ.
Its initial de Broglie wavelength is λ0.
The de Broglie wavelength at time t is given by: λ0/(1+(eEt/m v0^2))^1/2.
Where:
- e is the electron charge
- E is the electric field strength
- m is the electron mass
- t is the time
- v0 is the initial velocity

This quiz explores key topics in quantum physics, including de Broglie wavelength, the photoelectric effect, and atomic spectra. Test your understanding of electron energy levels, photon interactions, and the corresponding wavelengths of the Balmer series. Perfect for students studying advanced physics concepts.