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3 years ago

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g Radiation of an unknown wavelength is used in a photoelectric effect experiment on a sodium surface. The maximum kinetic energ

y of the observed electrons is 0.7 eV. What is the wavelength of the light

1 answer:

Andreas93 [3]3 years ago

4 0

Answer:

λ = 4.1638 10⁻⁷ m

Explanation:

The photoelectric effect was explained by Einstein assuming that the radiation acts like particles and the equation that describes the process is

K = h f -Ф

where K is the kinetic energy of the emitted electrons, hf the energy of the photons according to Planck's equation and Ф the work function of the material

In this case they give us the kinetic energy of the electrons

K = 0.7 eV

The sodium work function is tabulated Ф = 2.28 eV

Let's find the frequency of the photons

f = (K + Ф) / h

Planck's constant is

h = 6.626 10⁻³⁴ J s (1 eV / 1.6 10⁻¹⁹ J) = 4.136 10⁻¹⁵ eV s

f = (0.7 + 2.28) / 4.136 10⁻¹⁵

f = 7.2050 10¹⁴ Hz

let's find the wavelength using the relationship between speed and frequency and wavelength

c = λ f

λ = c / f

λ = 3 10⁸ / 7.205 10¹⁴

λ = 4.1638 10⁻⁷ m

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Answer : The values of $\Delta H^o,\Delta S^o\text{ and }\Delta G^o$ are $62.2kJ,132.67J/K\text{ and }22.66kJ$ respectively.

Explanation :

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Now put all the given values in this expression, we get:

$\Delta H^o=[4mole\times (0kJ/mol)+1mole\times (0kJ/mol)}]-[2mole\times (-31.1kJ/mol)]$

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conversion used : (1 kJ = 1000 J)

Now we have to calculate the entropy of reaction $(\Delta S^o)$ .

$\Delta S^o=S_f_{product}-S_f_{product}$

$\Delta S^o=[n_{Ag}\times \Delta S_f^0_{(Ag)}+n_{O_2}\times \Delta S_f^0_{(O_2)}]-[n_{Ag_2O}\times \Delta S_f^0_{(Ag_2O)}]$

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Now put all the given values in this expression, we get:

$\Delta S^o=[4mole\times (42.55J/K.mole)+1mole\times (205.07J/K.mole)}]-[2mole\times (121.3J/K.mole)]$

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Now we have to calculate the Gibbs free energy of reaction $(\Delta G^o)$ .

As we know that,

$\Delta G^o=\Delta H^o-T\Delta S^o$

At room temperature, the temperature is 298 K.

$\Delta G^o=(62200J)-(298K\times 132.67J/K)$

$\Delta G^o=22664.34J=22.66kJ$

Therefore, the values of $\Delta H^o,\Delta S^o\text{ and }\Delta G^o$ are $62.2kJ,132.67J/K\text{ and }22.66kJ$ respectively.

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