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What is the ratio of the de-Broglie wavelength associated with an electron and the wavelength of a photon with the same energy E?
What is the ratio of the de-Broglie wavelength associated with an electron and the wavelength of a photon with the same energy E?
- $\frac{1}{2} \sqrt{\frac{E}{2m}}$ (correct)
- $c(2mE)^{1/2}$
- $\frac{c}{\sqrt{2mE}}$ (correct)
- $\frac{1}{2} \sqrt{\frac{2E}{m}}$
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?
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?
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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?
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?
- 5.6 × 10^15 (correct)
- 6.2 × 10^15
- 1.6 × 10^15
- 7.8 × 10^14
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 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?
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 Ã…?
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 Ã…?
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Study Notes
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 Ã….
- 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
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