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.

not quite sure how to do this.

Potential energy gain = q V = m g h

V = m g h/q

V = 9.1 * 10^-28*10^-3 * 9.8 *5*10^-2 / 1.6*10^-19

Hi Damon .. where did the 10^-3 come from? .. I understand the 9.8 is gravity and the 5 is 5 cm

Damon used kg for mass and meters for distance. Those units go with the 9.8 m/s^2 for g. The 10^-3 and 10^-2 are conversion factors from grams and cm.

To calculate the voltage required to lift an electron, we can follow these steps:

Step 1: Convert the mass of the electron from grams to kilograms.
The mass of the electron is given as 9.1 x 10^-28 grams. To convert grams to kilograms, divide the mass by 1,000 since there are 1,000 grams in a kilogram.
Mass of electron = 9.1 x 10^-28 grams / 1,000 = 9.1 x 10^-31 kilograms

Step 2: Calculate the gravitational potential energy.
The gravitational potential energy can be calculated using the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
In this case, the height is given as 5 cm, which needs to be converted to meters by dividing it by 100 since there are 100 centimeters in a meter.
Height (h) = 5 cm / 100 = 0.05 meters.
Acceleration due to gravity (g) can be approximated as 9.8 m/s^2.
Potential energy (PE) = mass (m) x gravity (g) x height (h)
PE = (9.1 x 10^-31 kg) x (9.8 m/s^2) x (0.05 m)

Step 3: Calculate the electrical potential energy.
The electrical potential energy can be calculated using the formula: PE = qV, where q is the charge on the electron and V is the voltage.
In this case, the charge on the electron is given as 1.6 x 10^-19 Coulombs.
Electrical potential energy (PE) = charge (q) x voltage (V)
PE = (1.6 x 10^-19 C) x V

Step 4: Equate the gravitational potential energy and electrical potential energy.
Since the electron is lifted to a certain height, the electrical potential energy should be equal to the gravitational potential energy.
(9.1 x 10^-31 kg) x (9.8 m/s^2) x (0.05 m) = (1.6 x 10^-19 C) x V

Step 5: Solve for V (voltage).
V = [(9.1 x 10^-31 kg) x (9.8 m/s^2) x (0.05 m)] / (1.6 x 10^-19 C)

By plugging in the given values and calculating the expression, you can find the voltage required to lift an electron 5 cm.