TO WHAT SPEED MUST AN ELECTRON BE ACCELERATED FOR IT TO HAVE A WAVELENGTH OF 3.0CM?
Use the DeBroglie equation.
wavelength = h/mv
To determine the speed at which an electron must be accelerated to have a specific wavelength, we can make use of the de Broglie wavelength equation. This equation relates the wavelength (λ) of a particle to its momentum (p) and mass (m).
The de Broglie wavelength equation is given by:
λ = h / p
Where:
λ is the wavelength
h is the Planck's constant (approximately 6.626 x 10^-34 J·s)
p is the momentum of the particle
For an electron, the momentum (p) is given by:
p = m * v
Where:
m is the mass of the electron (approximately 9.11 x 10^-31 kg)
v is the velocity of the electron
Combining the two equations above, we can express the wavelength (λ) as:
λ = h / (m * v)
To find the speed (v) at which the electron must be accelerated, we can rearrange the equation as follows:
v = h / (m * λ)
Plugging in the values for Planck's constant (h), mass of the electron (m), and the desired wavelength (λ) of 3.0 cm (0.03 m), we can calculate the required speed (v).
v = (6.626 x 10^-34 J·s) / (9.11 x 10^-31 kg * 0.03 m)
Solving this equation will give us the speed at which the electron must be accelerated to have a wavelength of 3.0 cm.
The wavelength of an electron can be calculated using the de Broglie equation:
λ = h / mv
where λ is the wavelength, h is the Planck's constant (6.62607015 × 10^-34 m^2 kg / s), m is the mass of the electron (9.10938356 × 10^-31 kg), and v is the speed of the electron.
To find the speed of the electron required for a wavelength of 3.0 cm, we need to convert the wavelength to meters:
λ = 3.0 cm = 3.0 × 10^-2 m
Now, we can rearrange the de Broglie equation to solve for v:
v = h / (mλ)
v = (6.62607015 × 10^-34 m^2 kg / s) / (9.10938356 × 10^-31 kg × 3.0 × 10^-2 m)
v ≈ 2.32 × 10^6 m/s
Therefore, the electron must be accelerated to a speed of approximately 2.32 × 10^6 m/s to have a wavelength of 3.0 cm.