A metal surface is exposed to 500nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 × 10¹⁴ Hz. The velocity of ejected electron is_______× 10⁵ ms^-1. (Nearest integer)

[Use : h = 6.63 × 10^-34 Js, m_e = 9.0 × 10^-31 kg]

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alok kumar singh | Contributor-Level 10

3 months ago

In photo-electric effect;

$\frac{h c}{λ} = h v_{0} + \frac{1}{2} m v^{2}$

$\frac{6.63 \times 1 0^{- 34} \times 3 \times 1 0^{8}}{500 \times 1 0^{- 9}} = (6.63 \times 1 0^{- 34} \times 4.3 \times 1 0^{14}) + \frac{1}{2} \times 9.0 \times 1 0^{- 31} \times v^{2}$

$v = \sqrt[]{\frac{(3.978 \times 1 0^{- 19} - 2.85 \times 1 0^{- 19})}{4.5 \times 1 0^{- 31}}} = \sqrt[]{25 \times 1 0^{10}} = 5 \times 1 0^{5} m / s$

Ans. = 5

In photo-electric effect;  <math> <mrow> <mfrac> <mrow> <mi>h</mi> <mi>c</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>=</mo> <mi>h</mi> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math>               <math> <mrow> <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>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> </mrow> <mrow> <mn>5</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>9</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mrow> <mo>(</mo> <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>4</mn> <mo>.</mo> <mn>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>4</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mn>9</mn> <mo>.</mo> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> <mn>1</mn> </mrow> </msup> <mo>×</mo> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math>              <math> <mrow> <mi>v</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mo>.</mo> <mn>9</mn> <mn>7</mn> <mn>8</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>9</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mo>.</mo> <mn>8</mn> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>9</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>4</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mn>2</mn> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>5</mn> </mrow> </msup> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math>             Ans. = 5

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A metal surface is exposed to 500nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 × 10¹⁴ Hz. The velocity of ejected electron is_______× 10⁵ ms^-1. (Nearest integer)

[Use : h = 6.63 × 10^-34 Js, m_e = 9.0 × 10^-31 kg]

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A metal surface is exposed to 500nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 × 1014 Hz. The velocity of ejected electron is_______× 105 ms-1. (Nearest integer) [Use : h = 6.63 × 10-34 Js, me = 9.0 × 10-31 kg]

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A metal surface is exposed to 500nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 × 10¹⁴ Hz. The velocity of ejected electron is_______× 10⁵ ms^-1. (Nearest integer)

[Use : h = 6.63 × 10^-34 Js, m_e = 9.0 × 10^-31 kg]