Work function of sodium is 2.35eV. What is the threshold wavelength an...
**Threshold Wavelength and Frequency:**
The work function of sodium is given as 2.35 eV. To find the threshold wavelength and frequency of light that causes the photoelectrons to be emitted, we can use the equation:
E = hf - φ
where E is the energy of the incident photon, h is the Planck's constant (6.626 x 10^-34 J.s), f is the frequency of the incident light, and φ is the work function.
First, we need to convert the work function from electron volts (eV) to Joules (J). We know that 1 eV is equal to 1.6 x 10^-19 J. Therefore, the work function in Joules is:
φ = 2.35 eV * (1.6 x 10^-19 J/eV) = 3.76 x 10^-19 J
Next, we can rearrange the equation to solve for the frequency:
f = (E + φ) / h
Since we are looking for the threshold frequency, the energy of the incident photon is equal to the work function:
E = φ = 3.76 x 10^-19 J
Substituting the values into the equation, we get:
f = (3.76 x 10^-19 J + 3.76 x 10^-19 J) / (6.626 x 10^-34 J.s) ≈ 1.13 x 10^15 Hz
The threshold frequency is approximately 1.13 x 10^15 Hz.
To find the threshold wavelength, we can use the equation:
c = λf
where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength.
Rearranging the equation to solve for the wavelength, we get:
λ = c / f = (3 x 10^8 m/s) / (1.13 x 10^15 Hz) ≈ 2.66 x 10^-7 m
The threshold wavelength is approximately 2.66 x 10^-7 m or 266 nm.
**Maximum Kinetic Energy of Photoelectrons:**
To calculate the maximum kinetic energy of photoelectrons, we can use the equation:
E = hf - φ
where E is the energy of the incident photon, h is the Planck's constant (6.626 x 10^-34 J.s), f is the frequency of the incident light, and φ is the work function.
The energy of the incident photon can be calculated using the equation:
E = hc / λ
where h is the Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the incident light.
Substituting the values into the equation, we get:
E = (6.626 x 10^-34 J.s) * (3 x 10^8 m/s) / (1000 x 10^-10 m) = 1.99 x 10^-19 J
Next, we can calculate the maximum kinetic energy of photoelectrons:
E = hf - φ
E = (6.626 x 10^-34 J.s) * (1.13 x 10^15 Hz) - (3.76 x 10^-
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.