Question

Pieces of potassium (Φ = 3.68 × 10–19 J) and sodium (Φ = 4.41 × 10–19 J) metal are exposed to radiation of wavelength 290.0 nm.

What is the velocity of the electrons from sodium?

What is the velocity of the electrons from potassium?

Answer 1

Answer:The velocity of electrons from sodium and potassium can be calculated using the equation E=hf, where E is the energy of the electron, h is Planck's constant and f is the frequency of the radiation.

From the equation E=hf, f can be calculated using the wavelength of the radiation:

f = c/λ

where c is the speed of light.

Then, using E=hf and the values for E (Φ) for sodium and potassium, the velocity of the electrons can be calculated using the equation:

v = sqrt(2E/m)

where m is the mass of the electron.

Step-by-step explanation:

The velocity of electrons from sodium and potassium can be calculated using the equation E=hf, where E is the energy of the electron, h is Planck's constant and f is the frequency of the radiation.

From the equation E=hf, f can be calculated using the wavelength of the radiation:

f = c/λ

where c is the speed of light.

Then, using E=hf and the values for E (Φ) for sodium and potassium, the velocity of the electrons can be calculated using the equation:

v = sqrt(2E/m)

where m is the mass of the electron.

Answer 2

Step-by-step explanation:

The velocity of electrons can be calculated using the equation v = h / (mλ), where h is Planck's constant (6.63 x 10^-34 Js), m is the mass of the electron, and λ is the wavelength of the radiation.

For sodium, the electron energy is given as Φ = 4.41 × 10–19 J. To find the velocity of the electrons, we first need to convert the energy into wavelength using the equation λ = hc / Φ, where c is the speed of light (3 x 10^8 m/s).

So, for sodium:

λ = hc / Φ = 6.63 x 10^-34 x 3 x 10^8 / 4.41 x 10^-19

λ = 290 nm.

And then using the velocity equation,

v = h / (mλ) = 6.63 x 10^-34 / (9.11 x 10^-31 x (290 x 10^-9))

For potassium, the electron energy is given as Φ = 3.68 × 10–19 J, and the wavelength can be calculated in the same way as for sodium:

λ = hc / Φ = 6.63 x 10^-34 x 3 x 10^8 / 3.68 x 10^-19

λ = 290 nm.

And then using the velocity equation,

v = h / (mλ) = 6.63 x 10^-34 / (9.11 x 10^-31 x (290 x 10^-9))

Note: m is the mass of an electron, which is 9.11 x 10^-31 kg.

So, both the velocity of the electrons from sodium and potassium would be the same, given that they are both exposed to the same wavelength radiation of 290 nm.