A proton and a Li³⁺ nucleus are accelerated by the same potential. If $λ_{L i} a n d λ_{P}$ denote the de Brogle wavelength of Li³⁺ and proton respectively, then the value of $\frac{λ_{L i}}{λ_{P}} i s x \times 1 0^{- 1} .$ The value of x is_________ (Rounded off to the nearest integer) [Mass of Li³⁺ = 8.3 mass of proton]

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alok kumar singh | Contributor-Level 10

a month ago

Using $λ = \frac{h}{\sqrt[]{2 q V m}}$

$λ_{L i} = \frac{h}{\sqrt[]{2 \times 3 e \times V \times 8.3 m}}$ m = mass of proton

$λ_{p} = \frac{h}{\sqrt[]{2 \times e \times V \times m}}$

$\frac{λ_{L i}}{λ_{p}} = \sqrt[]{\frac{2 e V m}{2 \times 24.9 e V m}}$

= 0.2 = 2 × 10^-1

So; x = 2

Using <math> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> <mi>q</mi> <mi>V</mi> <mi>m</mi> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816691926"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>L</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> <mo>×</mo> <mn>3</mn> <mi>e</mi> <mo>×</mo> <mi>V</mi> <mo>×</mo> <mn>8</mn> <mo>.</mo> <mn>3</mn> <mi>m</mi> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math>           <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816691927"> </o:OLEObject></xml><! [endif]->      m = mass of proton<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816691957"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> <mo>×</mo> <mi>e</mi> <mo>×</mo> <mi>V</mi> <mo>×</mo> <mi>m</mi> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math>   <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>L</mi> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>e</mi> <mi>V</mi> <mi>m</mi> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> <mn>4</mn> <mo>.</mo> <mn>9</mn> <mi>e</mi> <mi>V</mi> <mi>m</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>           <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816691958"> </o:OLEObject></xml><! [endif]-> = 0.2 = 2 × 10-1So; x = 2

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