Respuesta :
B = magnetic field in the cyclotron = 0.400 T
q = magnitude of charge on a proton = 1.6 x 10⁻¹⁹ C
m = mass of the proton = 1.67 x 10⁻²⁷ kg
f = frequency of revolution of proton in the cyclotron = ?
v = speed of electromagnetic waves = 3 x 10⁸ m/s
λ = wavelength of electromagnetic wave = ?
Frequency of revolution of proton in the cyclotron is given as
f = qB/(2πm)
inserting the values
f = (1.6 x 10⁻¹⁹)(0.400)/(2 (3.14) (1.67 x 10⁻²⁷))
f = 6.1 x 10⁶ Hz
wavelength of electromagnetic wave is given as
λ = v/f
λ = (3 x 10⁸)/(6.1 x 10⁶)
λ = 49.2 m
The wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.400 t is [tex]49.19[/tex]
Explanation:
Electromagnetic radiation is the electromagnetic field waves that propagates through space and carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays.
A proton is a subatomic particle with symbol p or p⁺ with positive electric charge of +1e elementary charge and a mass slightly less than neutron.
A cyclotron a type of particle accelerator that accelerates charged particles outwards from the center along a spiral path.
Accelerating charges radiate electromagnetic waves. calculate the wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.400 t.
- B = magnetic field in the cyclotron = 0.400 T
- q = magnitude of charge on a proton = 1.6 x 10⁻¹⁹ C
- m = mass of the proton = 1.67 x 10⁻²⁷ kg
- f = frequency of revolution of proton in the cyclotron
- v = speed of electromagnetic waves = 3 x 10⁸ m/s
[tex]\omega=\frac{v}{\rho} = \frac{qB}{m} = \frac{1.6*10^{-19}C * 0.4t}{1.67*10^{-27} kg}\\\omega = \frac{0.64*10^{-19} Ct }{1.67*10^{-27} kg} = 0.383 * 10^{8}[/tex]
[tex]T = \frac{2*\pi}{\omega} = \frac{2*\pi}{0.383*10^{8}} = 16.396*10^{-8}[/tex]
[tex]\omega = \frac{2\pi c}{\lambda} \\ 0.383*10^8= \frac{2\pi * 3*10^{8}}{\lambda} \\\lambda = \frac{18.84}{0.383} = 49.19[/tex]
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