A stationary hydrogen atom de excites from first excited state to ground state. Find recoil speed of hydrogen atom up to nearest integral value, (mass of hydrogen atom
= 1.8 × 10^–27 kg)

$\left|\Delta E_0\right|=\left(-136\left\{1-\frac{1}{4}\right\}\right)eV$

|DE₀| = –10.2

$\lambda =\frac{12400}{10.2}\times 10^{-10}m$

$\rho =\frac{h}{\lambda }=\frac{6.63\times 10^{-34}\times 10.2}{12400\times 10^{-10}}$                  

$?$ $mv=\frac{h}{\lambda }$            

  $1.8\times 10^{-27}$           

$v=\frac{6.63\times 10.2\times 10^{-34}}{12400\times 10^{-10}}$

$v=\frac{6.63\times 10.2}{12400\times 1.8}\times 10^3$            

$=\frac{6.63\times 102}{124\times 1.8}=3.02$ ]

= 3 m/s

<p><span lang="EN-IN"> &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820663435"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mrow> <mo>|</mo> <mrow> <mi>Δ</mi> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> <mn>3</mn> <mn>6</mn> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mi>e</mi> <mi>V</mi> </mrow> </math> </span></span></p><p><span lang="EN-IN">|</span><span lang="EN-IN">D</span><span lang="EN-IN">E₀| = –10.2</span></p><div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1759138099phprxSRqP.jpeg" alt="" width="283" height="115" loading="lazy"></picture></div></div><p><span contenteditable="false"> <math> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mn>2</mn> <mn>4</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> </mrow> </msup> <mtext> </mtext> <mi>m</mi> </mrow> </math> </span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mi>ρ</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mn>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> <mn>4</mn> </mrow> </msup> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mn>2</mn> <mn>4</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mo>?</mo> </mrow> </math> </span><span contenteditable="false"> <math> <mrow> <mi>m</mi> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820663436"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;</span></p><p><span lang="EN-IN"> &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820663443"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;</span></p><p><span lang="EN-IN">&nbsp; <span contenteditable="false"> <math> <mrow> <mn>1</mn> <mo>.</mo> <mn>8</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> <mn>7</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820663444"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp; &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820663445"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;</span></p><p><span contenteditable="false"> <math> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mn>3</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mn>2</mn> <mn>4</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mn>3</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mn>2</mn> <mn>4</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <mo>.</mo> <mn>8</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1820663447"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;</span></p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mn>3</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mn>2</mn> <mn>4</mn> <mo>×</mo> <mn>1</mn> <mo>.</mo> <mn>8</mn> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mo>.</mo> <mn>0</mn> <mn>2</mn> </mrow> </math> </span> ]</p><p><span lang="EN-IN">= 3 m/s</span></p>

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