Explanation- velocity of a freely falling body is v= $\sqrt[]{2gh}$

And $\lambda =\frac{h}{mv}=\frac{h}{m\sqrt[]{2gh}}$

$\lambda =h$ -1

 The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly
a) 1.2 nm (b) 1.2 x 10-3 nm
(c) 1.2 x 10-6  nm (d). 1.2 x 10 nm

(d)

We can write

OS + PS > OP …….(i)

OS > PS – OP …….(ii)

$\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ $>$ $\left|\stackrel{?}{a}\right|$ + $\left|\stackrel{?}{b}\right|$ ….(iii)

The quantity on the LHS is always positive and that on the RHS can be positive or negative. To make both quantities positive, we take modulus of both sides as:

$\left|\left|\stackrel{?}{a}-\stackrel{?}{b}\right|\right|$ > $\left|\left|\stackrel{?}{a}\right|-\mathrm{}\mathrm{}\left|\stackrel{?}{b}\right|\mathrm{}\right|$ ….(iv)

If the two vectors $\stackrel{?}{a}$ and $\stackrel{?}{b}$ act along a straight line but in the opposite direction, then we can write $\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ = $\left|\stackrel{?}{a}\right|$ - $\left|\stackrel{?}{b}\right|\dots ..\left(v\right)$

Combining (iv) and (v), we get

$\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ $\ge$ $\left|\stackrel{?}{a}\right|$ - $\left|\stackrel{?}{b}\right|$

<p><strong>(d)</strong></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1728971091php85fXyf_480x360.jpeg" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1728971091php85fXyf.jpeg" alt="" width="207" height="154"></picture></div></div><p>We can write</p><p>OS + PS &gt; OP …….(i)</p><p>OS &gt; PS – OP …….(ii)</p><p><span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover><mo>-</mo><mi></mi><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover><mi></mi></mrow></mrow></mfenced></math></span>&nbsp;<span title="Click to copy mathml"><math><mo>&gt;</mo></math></span>&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced></math></span>&nbsp;+&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced></math></span>&nbsp;….(iii)</p><p>The quantity on the LHS is always positive and that on the RHS can be positive or negative. To make both quantities positive, we take modulus of both sides as:</p><p><span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover><mo>-</mo><mi></mi><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover><mi></mi></mrow></mrow></mfenced></mrow></mrow></mfenced></math></span>&nbsp;&gt;&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced><mo>-</mo><mi mathvariant="normal"></mi><mi mathvariant="normal"></mi><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced><mi mathvariant="normal"></mi></mrow></mrow></mfenced><mi></mi></math></span>&nbsp;….(iv)</p><p>If the two vectors&nbsp;<span title="Click to copy mathml"><math><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover><mi></mi></math></span>&nbsp;and&nbsp;<span title="Click to copy mathml"><math><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover></math></span>&nbsp;act along a straight line but in the opposite direction, then we can write&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover><mo>-</mo><mi></mi><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover><mi></mi></mrow></mrow></mfenced></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced></math></span>&nbsp;-&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced><mo>…</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>v</mi><mo>)</mo></math></span></p><p>Combining (iv) and (v), we get</p><p><span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover><mo>-</mo><mi></mi><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover><mi></mi></mrow></mrow></mfenced></math></span>&nbsp;<span title="Click to copy mathml"><math><mo>≥</mo></math></span>&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>a</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced></math></span>&nbsp;-&nbsp;<span title="Click to copy mathml"><math><mfenced open="|" close="|" separators="|"><mrow><mrow><mover accent="true"><mrow><mrow><mi>b</mi></mrow></mrow><mo>?</mo></mover></mrow></mrow></mfenced></math></span></p>

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