91影视

For the average kinetic energy of the particle$\frac{\mathbf{\text{3}}}{\mathbf{\text{2}}}{\mathbf{\text{k}}}_{\mathbf{\text{B}}}\mathbf{\text{T}}$ , the wavelength of the particle of mass m can be given as,

$\mathit{位}\mathbf{\text{=}}\frac{\mathbf{\text{h}}}{\sqrt{{\mathbf{\text{3mk}}}_{\mathbf{\text{B}}}\mathbf{\text{T}}}}$鈥︹赌︹赌︹赌︹赌︹赌︹赌�..(1)

$\begin{array}{c}\text{位}=\frac{\text{h}}{\sqrt{{\text{3m}}_{\text{n}}{\text{k}}_{\text{B}}\text{T}}}\\ =\frac{{\text{6.63脳10}}^{\text{-34}}\text{鈥塉}鈰�\text{s}}{\sqrt{\text{3}脳(\text{1.6750}脳{\text{10}}^{\text{-27}}\text{kg})脳(\text{1.38}脳{\text{10}}^{\text{-23}}\text{鈥�}J/K)脳\text{300K}}}\\ =\text{1.456}脳{\text{10}}^{\text{-10}}\text{鈥尘}\end{array}$

Using the de-Broglie Relationship,

$\begin{array}{c}\text{位}=\frac{\text{h}}{\text{p}}\\ =\frac{\text{h}}{{\text{m}}_{\text{n}}脳\text{0.01c}}\\ =\frac{\text{6.63}脳{\text{10}}^{\text{-34}}\text{鈥塉}鈰�\text{s}}{(\text{1.67}脳{\text{10}}^{\text{-27}}\text{鈥塳驳})脳(\text{3}脳{\text{10}}^{\text{6}}\text{m/s})}\\ =\text{1.32}脳{\text{10}}^{\text{-13}}\text{m}\end{array}$

Step 2:Analysis of mass of the electron

(b)

Do the same analysis as in part (a), but this time use the electron's mass.

$\begin{array}{c}\text{位}=\frac{\text{h}}{\sqrt{{\text{3m}}_{\text{e}}{\text{k}}_{\text{B}}\text{T}}}\\ =\frac{\text{6.63}脳{\text{10}}^{\text{-34}}\text{鈥塉}鈰�\text{s}}{\sqrt{\text{3}脳(\text{9.1}脳{\text{10}}^{\text{-31}}\text{kg})脳(\text{1.38}脳{\text{10}}^{\text{-23}}\text{鈥�}J/K)脳\text{300K}}}\\ =\text{6.236}脳{\text{10}}^{\text{-9}}\text{鈥尘}\end{array}$

Using the de-Broglie Relationship,

$\begin{array}{c}\text{位}=\frac{\text{h}}{\text{p}}\\ =\frac{\text{h}}{{\text{m}}_e脳\text{0.01c}}\\ =\frac{\text{6.63}脳{\text{10}}^{\text{-34}}\text{鈥塉}鈰�\text{s}}{(9.1脳{\text{10}}^{\text{-31}}\text{鈥塳驳})脳(\text{3}脳{\text{10}}^{\text{6}}\text{m/s})}\\ =\text{2.43}脳{\text{10}}^{\text{-10}}\text{m}\end{array}$

(c)

When the dimension of the slit is approximately near to their wavelength, each particle will behave as a wave, e.g. diffracted from a single slit. The neutron's wave properties will be revealed in the region of about$\text{0.1nm}$to$\text{0.0001nm}$, however, the electron will vary from$\text{0.2nm}$to $\text{6.0nm}$. You may observe that the electron range is significantly smaller than that of the neutron; this is due to the mass difference between them.

Because the electron is already traveling at high speeds at ambient temperature, the given speed isn't far from the genuine value.

Therefore,

a)$\text{1.456}脳{\text{10}}^{\text{-10}}\text{鈥尘to鈥�1.32}脳{\text{10}}^{\text{-13}}\text{鈥尘}$

b)$\text{6.236}脳{\text{10}}^{\text{-9}}\text{鈥尘鈥塼o鈥�2.43}脳{\text{10}}^{\text{-10}}\text{鈥尘}$

c) In the region of roughly, the neutron's wave characteristic will be revealed $\text{0.1nm}$to$\text{0.0001nm}$ , however, the electron will vary from$\text{0.2nm}$ to$\text{6.0nm}$