Final answer:
The wavelength of an electron moving with a velocity of 2.5 x 10⁸ cm/s is calculated using the de Broglie equation and is approximately 2.91 x 10⁻¹ meters.
Step-by-step explanation:
To calculate the wavelength of an electron moving with a velocity of 2.5 x 10⁸ cm/s, we can use the de Broglie equation, which relates an electron's wavelength to its momentum (p). The de Broglie equation is given by λ = h/p, where h is Planck's constant (6.626 x 10⁻³⁴ Js) and p is the momentum of the electron.
The momentum of an electron (p) can be found using the equation p = mv, where m is the mass of the electron, and v is its velocity. Given the electron mass (9.11 x 10⁻³ⁱ kg), we can calculate p.
First, we need to convert the velocity of the electron from cm/s to m/s by multiplying by 10⁻²:
v = 2.5 x 10⁸ cm/s x 10⁻² = 2.5 x 10⁶ m/s
Then, we can calculate the momentum:
p = (9.11 x 10⁻³ⁱ kg)(2.5 x 10⁶ m/s) = 2.2775 x 10⁻²⁴ kg m/s
Finally, using de Broglie's equation, we find the wavelength:
λ = h/p
λ = (6.626 x 10⁻³⁴ Js) / (2.2775 x 10⁻²⁴ kg m/s)
λ = 2.91 x 10⁻¹ m
The wavelength of the electron moving at the given velocity is approximately 2.91 x 10⁻¹ meters.