In a typical electron microscope, the momentum of each electron is about 1.4 10-22 kg-m/s. What is the de Broglie wavelength of the electrons?
Simple. All you need is this equation:
λ = h/p
So, just plug numbers in...
λ = (6.63 x 10^-34 J*s) / (1.4 x 10^-22 kg-m/s)
λ = 4.74 x 10^-12 m
Simple. All you need is this equation:
λ = h/p
So, just plug numbers in...
λ = (6.63 x 10^-34 J*s) / (1.4 x 10^-22 kg-m/s)
λ = 4.74 x 10^-12 m
To find the de Broglie wavelength of the electrons, we can use the following formula:
λ = h / p
where λ is the de Broglie wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum of the electrons.
Given that the momentum of each electron is 1.4 x 10^-22 kg·m/s, we can substitute this value into the formula and calculate the de Broglie wavelength.
λ = (6.626 x 10^-34 J·s) / (1.4 x 10^-22 kg·m/s)
λ ≈ 4.76 x 10^-12 m
Therefore, the de Broglie wavelength of the electrons in a typical electron microscope is approximately 4.76 x 10^-12 meters.
To find the de Broglie wavelength of an electron, we can use the de Broglie equation, which relates the momentum (p) of a particle to its wavelength (λ). The equation is as follows:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck constant (approximately 6.626 × 10^-34 J·s), and p is the momentum of the particle.
Given the momentum of each electron as 1.4 × 10^-22 kg·m/s, we can substitute these values into the equation to find the de Broglie wavelength.
λ = (6.626 × 10^-34 J·s) / (1.4 × 10^-22 kg·m/s)
First, we can simplify the units:
1 J·s = 1 kg·m^2/s^2
λ = (6.626 × 10^-34 kg·m^2/s) / (1.4 × 10^-22 kg·m/s)
Next, we can cancel out the units of kg and m:
λ = (6.626 × 10^-34 m^2/s) / (1.4 × 10^-22 s)
Now we can perform the division:
λ = (6.626 × 10^-34) / (1.4 × 10^-22) m
Simplifying further:
λ = 4.732 × 10^-12 m
Therefore, the de Broglie wavelength of the electrons is approximately 4.732 × 10^-12 meters.