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Answer:
K = 13448.64eV
Explanation:
(a) In order to calculate the kinetic energy of the electrons, to "see" the atom, you take into account that the wavelength of the electrons must be of the order of the resolution required (0.010nm).
Then, you first calculate, by using the Broglies' relation, the momentum of the electron associated to a wavelength of 0.010nm:
(1)
p: momentum of the electron
h: Planck's constant = 6.626*10^-34 Js
λ: wavelength = 0.010nm
You replace the values of the parameters in the equation (1):
With this values of the momentum of the electron you can calculate the kinetic energy of the electron by using the following formula:
(2)
m: mass of the electron = 9.1*10^-31 kg
In electron volts you obtain:
The kinetic energy required for the electrons must be, at least, of 13448.64 eV
(a) 0.714 cm
First of all, we need to find the spring constant of the spring. This can be done by using Hooke's law:
where
F is the force applied on the spring
k is the spring constant
x is the stretching of the spring
At the beginning, the force applied is the weight of the block of m = 4.20 kg hanging on the spring, therefore:
The stretching of the spring due to this force is
x = 2.00 cm = 0.02 m
Therefore, the spring constant is
Now, a new object of 1.50 kg is hanging on the spring instead of the previous one. So, the weight of this object is
And so, the stretching of th spring in this case is
(b) 1.65 J
The work done on a spring is given by:
where
k is the spring constant
x is the stretching of the spring
In this situation,
k = 2060 N/m
x = 4.00 cm = 0.04 m is the stretching due to the external agent
So, the work done is