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It takes 208.4 kJ of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? what is the maximum wavelength capable of doing this

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IthaloAbreu

Answer:

Energy: 3.46x10⁻¹⁹ J

Wavelength: 574.0 nm

Explanation:

For the Avogadros' number, we know that 1 mol of electron has 6.02x10²³ electrons, so

6.02x10²³ electrons ---------- 208.4 kJ

1 electron --------------------------- x

By a simple direct three rule:

6.02x10²³ x = 208.4

x = 3.46x10⁻²² kJ

Knowing that 1 kJ = 10³ J

E = 3.46x10⁻²²x10³ = 3.46x10⁻¹⁹ J

The energy is related to the wavelenght of the electron by the equation:

E = hxc/λ

Where h is the Planck consant (h = 6.626x10⁻³⁴ m²kg/s), c is the light velocity (c = 3.00x10⁸ m/s), and λ is the wavelenght. So:

3.46x10⁻¹⁹= (6.626x10⁻³⁴x3.00x10⁸)/λ

λ = 5.74x10⁻⁷m

λ = 574.0 nm

onyebuchinnaji

The maximum wavelength capable of removing the electron is 574.5 nm.

The given parameters;

  • energy taken to remove 1 mole of electron = 208.4 kJ

The energy required to remove a single electron is calculated as follows;

[tex]E_n = \frac{208.4 \times 10^3}{6.02 \times 10^{23}} \\\\E_n = 3.46 \times 10^{-19} \ J[/tex]

The maximum wavelength of the electron is calculated as follows;

E = hf

[tex]E = h\frac{c}{\lambda}[/tex]

where;

  • h is Planck's constant
  • c is speed of light
  • λ is the wavelength

The wavelength is calculated as follows;

[tex]\lambda = \frac{hc}{E} \\\\\lambda = \frac{(6.626 \times 10^{-34} )\times (3\times 10^8)}{3.46\times 10^{-19}} \\\\\lambda = 5.745 \times 10^{-7} \ m\\\\\lambda = 574.5 \ nm[/tex]

Thus, the maximum wavelength capable of removing the electron is 574.5 nm.

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