A metal whose threshold frequency is 1.10×1015 s−1 emits an electron with a velocity of 6.53×105 m/s when radiation of 1.37×1015 s−1 strikes the metal. What is the mass of the electron?
Well, you see, when it comes to the mass of an electron, we don't really need to know its velocity or the frequency of the radiation. The mass of an electron is a constant value, approximately 9.11 × 10^-31 kilograms. So, there you have it, the mass of an electron is like a stubborn friend – it doesn't change, no matter the circumstances!
To find the mass of the electron, we can use the equation for the kinetic energy of an electron:
Kinetic energy = (1/2) * mass * velocity^2
First, let's convert the threshold frequency and radiation frequency to energy using Planck's equation:
Energy = Planck's constant * frequency
The threshold energy can be calculated as follows:
Threshold energy = Planck's constant * threshold frequency
Similarly, the energy of the radiation can be calculated as follows:
Radiation energy = Planck's constant * radiation frequency
Next, subtract the threshold energy from the radiation energy to find the kinetic energy of the electron:
Kinetic energy = Radiation energy - Threshold energy
Now we can rearrange the kinetic energy equation to solve for the mass of the electron:
mass = (2 * Kinetic energy) / velocity^2
Let's calculate the values step by step:
Step 1: Convert threshold frequency to energy
Threshold energy = Planck's constant * threshold frequency
Threshold energy = 6.63 × 10^-34 Js * 1.10 × 10^15 s^-1
Step 2: Convert radiation frequency to energy
Radiation energy = Planck's constant * radiation frequency
Radiation energy = 6.63 × 10^-34 Js * 1.37 × 10^15 s^-1
Step 3: Calculate the kinetic energy of the electron
Kinetic energy = Radiation energy - Threshold energy
Step 4: Calculate the mass of the electron
mass = (2 * Kinetic energy) / velocity^2
Now you can plug in the values and calculate the mass of the electron.