Final answer:
The escape speed of an electron launched from a charged glass sphere can be calculated using the formula escape speed = √(2*q*V/m), where q is the charge of the sphere, V is the voltage, and m is the mass of the electron. To find the voltage, we can use the formula V = q/(4*pi*ε*r), where ε is the permittivity of free space and r is the radius of the sphere. By substituting the given values and calculating, we can then determine the escape speed.
Step-by-step explanation:
To calculate the escape speed of an electron launched from the surface of a charged glass sphere, we can use the formula:
escape speed = √(2*q*V/m)
where q is the charge of the sphere, V is the voltage, and m is the mass of the electron.
Given: diameter of the sphere = 1.4 cm, charge of the sphere = 7.0 nC, radius of the sphere = 0.7 cm, voltage = unknown, electron mass = 9.1 x 10^-31 kg.
- Convert the diameter to radius by dividing it by 2: 1.4 cm ÷ 2 = 0.7 cm.
- Convert the charge to Coulombs by dividing it by 10^9: 7.0 nC ÷ 10^9 = 7.0 x 10^-9 C.
- Calculate the voltage using the formula: V = q/(4*pi*ε*r), where ε is the permittivity of free space (8.854 x 10^-12 C^2/N*m^2) and r is the radius of the sphere.
- Substitute the values into the formula: V = (7.0 x 10^-9)/(4*pi*(8.854 x 10^-12)*(0.7 x 10^-2)).
- Calculate the escape speed using the formula: escape speed = √(2*(7.0 x 10^-9)*V/(9.1 x 10^-31)).
- Round the answer to two significant figures and include the appropriate units (m/s).
Therefore, the escape speed of an electron launched from the surface of a 1.4-cm-diameter glass sphere charged to 7.0 nC is _________ m/s.