given that the mass of an electron is 9.1 x 10^-28 grams and the charge on an electron is 1.6 x 10^-19 Coulombs, calculate the voltage required to lift an electron 5 cm.
the question was previously answered, but I did'nt understand it .. could some show me again please.
Weight x Distance = (charge)*(Voltage difference)
M*g*X = e*V
Solve for V
e = 1.6*10^-19 C
g = 9.8 m/s^2 (on Earth)
X = 0.05 m
M = 9.1*10^-31 kg
V = 2.8*10^-12 volts
Sure, let's break down the steps to calculate the voltage required to lift an electron 5 cm.
Step 1: Determine the work done (W)
The work done to lift an electron against gravity can be calculated using the formula:
W = m * g * h
where:
- W is the work done
- m is the mass of the electron
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height or distance the electron is lifted (in meters)
Given that the question states the distance in centimeters, we need to convert it to meters. 5 cm is equal to 0.05 meters.
Step 2: Convert the mass to kilograms
The mass of the electron given is in grams, but we need to have it in kilograms to use the formula correctly. So, we divide the mass by 1000:
m = 9.1 x 10^-28 grams / 1000 = 9.1 x 10^-31 kilograms
Step 3: Calculate the work done
Using the values we have gathered, we can now calculate the work done:
W = (9.1 x 10^-31 kg) * (9.8 m/s^2) * (0.05 m)
Step 4: Calculate the voltage (V)
To calculate the voltage, we need to use the formula:
V = W / q
where:
- V is the voltage
- W is the work done
- q is the charge on the electron
Given that the charge on an electron is 1.6 x 10^-19 Coulombs, we can substitute this value into the formula:
V = (9.1 x 10^-31 kg * 9.8 m/s^2 * 0.05 m) / (1.6 x 10^-19 C)
Simplifying the equation will give us the answer.
Note: It's important to understand the underlying physics principles and units when solving such problems.