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What is the wavelength of an electron with a mass of 9.11 x 10^-31 kg and a speed of 2.5 x 10^6 m.s^-1.?

Answer 1

Owen Atkinson

Determine the electron's kinetic energy as the first step in the solution:

#K_E=1/2mv^2# #E= 1/2*9.11*10^(¯31)kg*(2.5*10^6 m/s)^2#

#E = 2.84687*10^(¯17)kg*m^2 s^(¯2)# (I kept some guard digits)

J will be used (for Joules) when I use this value that is slightly below.

Next, we'll determine the wavelength using the de Broglie equation:

#λ=h/p# #λ=h/sqrt(2Em)#

#λ=(6.626*10^(¯34)J*s)/sqrt(2*(2.84687*10^(¯17)J)*(9.11*10^(¯31)kg))#

You can now compute the final answer. To confirm, note that: (1) Planck's Constant is measured in Joule-seconds, and both values are in the numerator; and (2) the denominator has three values that follow the radical and are all under the radical sign.

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Answer 2

Levi Anderson

The electron has a wavelength of about (5.45 \times 10^{-11}) meters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.