A neutron beam of energy E scatters from atoms on a surface with a spacing d = 0.1 nm. The first maximum intensity in the reflected beam occurs at θ= 30°. What is the kinetic energy E of the beam in eV?

<p><strong>Explanation-&nbsp;</strong>given d= 0.1nm, &nbsp;<span contenteditable="false"><math><mi>? </mi></math>&nbsp;</span>=30⁰&nbsp;and n=1</p><p>According to bragg's law</p><p>2dsin&nbsp;<span contenteditable="false"><math><mi>? </mi></math>&nbsp;</span><em>=&nbsp;</em>n&nbsp;<span contenteditable="false"><math><mi>? </mi></math></span></p><p>2<span contenteditable="false">&nbsp;<math><mo>*</mo><mn>0.1</mn><mo>*</mo><mi>s</mi><mi>i</mi><mi>n</mi><mn>30</mn><mo>=</mo><mi>? </mi></math></span></p><p><span contenteditable="false"><math><mi>? </mi><mo>=</mo><mn>0.1</mn><mi>n</mi><mi>m</mi><mo>=</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>10</mn></mrow></mrow></msup></math></span></p><p><span contenteditable="false"><math><mi>? </mi><mo>=</mo><mfrac><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mi>m</mi><mi>v</mi></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mrow><mi>h</mi></mrow></mrow><mrow><mrow><mi>p</mi></mrow></mrow></mfrac></math></span></p><p>P=h/&nbsp;<span contenteditable="false"><math><mi>? </mi></math>&nbsp;</span>&nbsp;=&nbsp;<span contenteditable="false"><math><mfrac><mrow><mrow><mn>6.62</mn><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>34</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>10</mn></mrow></mrow></msup></mrow></mrow></mfrac></math>&nbsp;</span>= 6.62<span contenteditable="false">&nbsp;<math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>24</mn></mrow></mrow></msup></math>&nbsp;</span>kgm/s</p><p>k.E= 1/2mv²=<span contenteditable="false">&nbsp;<math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mfrac><mrow><mrow><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><msup><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mi>m</mi></mrow></mrow></mfrac></math>&nbsp;</span>=&nbsp;<span contenteditable="false"><math><mfrac><mrow><mrow><msup><mrow><mrow><mi>p</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></math>&nbsp;</span>= 0.21eV</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment