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The kinetic energy of an electron is $1.67 \times 10^{-17}\mathrm{J}$. Calculate the wavelength ($\lambda$) of the electron.

I know the formula $\lambda= \frac{h}{mv}$; where h is Planck's constant.

How do I find $\lambda$ without $v$ (velocity) and $m$ (mass)?

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The mass of electron is never given in question you should remember it. Mass of electron is $9.109 \times 10^{-31} \mathrm{kg}$.

Now read the question Kinetic Energy is given, so from that you can easily find velocity of electron.

$$K.E.=\frac{1}{2}mv^2$$

so You will get $v= 6 \times10^6 \mathrm{m/s}$

Now you can substitute value of m and v in formula $\lambda = \frac{h}{mv}$

You will get wave length of electron as $0.12 \times 10^{-9} \mathrm{m}= 0.12 \mathrm{nm}$

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You do not even need to laboriously calculate the velocity of the electron. All you require is the mass (which should be in your knowledge), and the kinetic energy - already given.

See, momentum P = mv; And kinetic energy = 1/2mv*v

Now, if you multiply and divide the KE expression by mass m, you get -

(1/2)(mv)(mv)*(1/m) = (1/2)P^2(1/m)

So, all from here, you can cross-multiply and find momentum directly, and hence substitute in de-Broglie's formula to find the wavelength of the electron.

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