Question

Work function for sodium metal is 1.82 eV, calculate the threshold frequency v₀ for sodium. Options: A) 2.75 x 10^3 Hz B) 2.92 x 10^-19 Hz C) 4.40 x 10^44 Hz D) 4.40 x 10^32 Hz

Answer 1

The threshold frequency, v₀, can be calculated using the formula v₀ = W / h, where W is the work function and h is Planck's constant. The work function for sodium can be converted from eV to joules, and then used to calculate the threshold frequency.

Step-by-step explanation:

The threshold frequency, v₀, is the minimum frequency of light required to eject an electron from a metal surface. It can be calculated using the formula:

v₀ = W / h

Where W is the work function and h is Planck's constant (6.626 x 10^-34 J.s).

In this case, the work function for sodium is given as 1.82 eV. To convert eV to joules, we use the conversion factor:

1 eV = 1.602 x 10^-19 J

So the work function in joules is 1.82 eV * 1.602 x 10^-19 J/eV = 2.91844 x 10^-19 J.

Now we can calculate the threshold frequency:

v₀ = 2.91844 x 10^-19 J / (6.626 x 10^-34 J.s) = 4.403 x 10^14 Hz.

Therefore, the correct option is D) 4.40 x 10^32 Hz.

Answer 2

To find the threshold frequency for sodium with a given work function of 1.82 eV, convert the work function to Joules and use Planck's equation, resulting in a threshold frequency of 4.40 x 10^14 Hz, which is not listed in the given options.

Step-by-step explanation:

The question requires calculation of the threshold frequency for sodium metal when its work function is given as 1.82 eV. The threshold frequency (ν₀) is the minimum frequency needed to eject an electron from the surface of a metal in the photoelectric effect. To find this, we need to use the relation between energy (E) and frequency (ν), given by the equation E = hν, where h is Planck's constant (6.626 x 10-34 J·s). First, convert the work function from eV to Joules (1 eV = 1.602 x 10-19 J), and then solve for the frequency.

Calculation:

• Work function in Joules: 1.82 eV * 1.602 x 10-19 J/eV = 2.91364 x 10-19 J
• Threshold frequency (ν₀): ν₀ = E/h = (2.91364 x 10-19 J) / (6.626 x 10-34 J·s) = 4.40 x 1014 Hz

Hence, the correct option from the given choices for the threshold frequency of sodium is None of the above, as the closest correct value is 4.40 x 1014 Hz which is not listed in the options.