Question

Calculate the de Broglie wavelength of: a) A person running across the room (assume 180 kg at 1 m/s) b) A 5.0 MeV proton

Answer 1

Answer:

a

$\lambda = 3.68 *10^{-36} \ m$

b

$\lambda_p = 1.28*10^{-14} \ m$

Explanation:

From the question we are told that

   The mass of the person is  $m = 180 \ kg$

    The speed of the person is  $v = 1 \ m/s$

    The energy of the proton is  $E_ p = 5 MeV = 5 *10^{6} eV = 5.0 *10^6 * 1.60 *10^{-19} = 8.0 *10^{-13} \ J$

Generally the de Broglie wavelength is mathematically represented as

      $\lambda = \frac{h}{m * v }$

Here  h is the Planck constant with the value

      $h = 6.62607015 * 10^{-34} J \cdot s$

So  

     $\lambda = \frac{6.62607015 * 10^{-34}}{ 180 * 1 }$

=> $\lambda = 3.68 *10^{-36} \ m$

Generally the energy of the proton is mathematically represented as

         $E_p = \frac{1}{2} * m_p * v^2_p$

Here $m_p$  is the mass of proton with value  $m_p = 1.67 *10^{-27} \ kg$

=>     $8.0*10^{-13} = \frac{1}{2} * 1.67 *10^{-27} * v^2$

=>   $v _p= \sqrt{\frac{8.0 *10^{-13}}{ 0.5 * 1.67 *10^{-27}} }$

=>   $v = 3.09529 *10^{7} \ m/s$

So

        $\lambda_p = \frac{h}{m_p * v_p }$

so    $\lambda_p = \frac{6.62607015 * 10^{-34}}{1.67 *10^{-27} * 3.09529 *10^{7} }$

=>     $\lambda_p = 1.28*10^{-14} \ m$