1. Calculate the permeability of electrons with energy of 0.1 eV and 0.5 eV respectively when penetrating a positional energy barrier of 1.0 eV in height and 100 pm in length by tunnel phenomenon.
k Attachment image=[2m(V-E)]^1/2
T={1+(e^kL-e^-kL)^2/16ε(1-ε)}^-1 (ε= E/V)
2. Explain the meaning of tunneling covered in the above problem with the wave and explain the difference between classical and quantum mechanics based on it.

16. Which of the following statements is false?

(a) Let S = {v1, v2, . . . , vm} be a subset of a vector space V with dim(V) = n. If m > n, then S is linearly dependent.

(b) If A is an m × n matrix, then dim Nul A = n.

(c) If B is a basis for some finite-dimensional vector space W, then the change of coordinates matrix PB is always invertible.

(d) dim(R17) = 17.

(e) If B1 and B2 are both bases for the same vector space, then B1 and B2 have the same number of vectors.

1)What potential difference is needed to stop an electron that has an initial velocity v=7.0×105m/sv=7.0×105m/s?

2)How strong is the electric field between the plates of a 0.80-μFμF air-gap capacitor if they are 3.0 mmmm apart and each has a charge of 72 μCμC ?

3)A 3700-pFpF air-gap capacitor is connected to a 30-V battery.If a piece of mica (K= 7) is placed between the plates, how much charge will flow from the battery?

How to shorten this "if-else" statements in R studio? Thank you sooo much!

fizzbuzz = function(v = NULL){
for (term in v){
if (is.infinite(term) != TRUE){
if (is.numeric(term)){
if (term == as.integer(term)){
if (term %% 3 == 0){
if (term %% 5 == 0){
print("FizzBuzz")}
else {
print("Fizz")
}
}
else if (term %% 5 == 0){
print("Buzz")
}
else {
print(term)
}
}
else {
print ("This number is not an integer.")
}
}
else {
print ("This is not a number, or this number was entered as a string.")
}
}
else {
print ("You must enter an integer for this function to work.")
}
}
}

Public health emphasizes the importance of safe home, work, and community environments. Reliable access to clean drinking water, a toilet, and fuel is critical for human health. Minimizing exposure to hazards and injuries at work is is also essential for safety and well-being. Watch the TED Talk video (the link is provided below), and discuss in this forum the related issues. Feel free to share with us your thoughts and give your personal examples and observations.

https://www.youtube.com/watch?v=FKBVwX8dVhI

https://www.youtube.com/watch?v=LlQXs0yofMs

Consider a particle that is confined by a one dimensional quadratic (harmonic) potential of the form U(x) = Ax2 (where A is a positive real number).

a) What is the Hamiltonian of the particle (expressed as a function of velocity v and x)?

b) What is the average kinetic energy of the particle (expressed as a function of T)?

c) Use the Virial Theorem (Eq. 1.46) to obtain the average potential energy of the particle.

d) What would the average kinetic and potential energies be if U(x) = Ax6?

Eq. 1.46: <V>/<K> = 2/n

Public health emphasizes the importance of safe home, work, and community environments. Reliable access to clean drinking water, a toilet, and fuel is critical for human health. Minimizing exposure to hazards and injuries at work is is also essential for safety and well-being. Watch the TED Talk video (the link is provided below), and discuss in this forum the related issues. Feel free to share with us your thoughts and give your personal examples and observations.

https://www.youtube.com/watch?v=FKBVwX8dVhI

https://www.youtube.com/watch?v=LlQXs0yofMs

A 26-turn circular coil has a diameter of 0.60 m. It is placed with its axis along the direction of a 50.0-?T magnetic field and then flipped through an angle of 180° in 0.170 s. Determine the average emf generated in the coil, and the magnitude of the emf at 0.085 s. [4.3 x 10-3 V, 6.8 x 10-3 V] (Note: Very few students got the second part correct, you need to find the function for emf with respect to time and plug in time t.)

A 230 V, 250 rpm, 100 A separately excited dc motor has an armature resistance of
0.5 Ω. The motor is connected to 230 V dc supply and rated dc voltage is applied
the field winding. It is driving a load whose torque-speed characteristic is given by

TL = 500 − 10ω

where ω is the speed in rad/sec and TL is the load torque in N-m. Find
(a) the steady state speed at which the motor will drive the load.
(b) the armature current.
Neglect the rotational losses of the machine.

Consider 45 risk-neutral bidders who are participating in a second-price, sealed-bid auction. It is commonly known that bidders have independent private values. Based on this information, we know the optimal bidding strategy for each bidder is to:

A. bid their own valuation of the item.

B. shade their bid to just below their own valuation.

C. bid according to the following bid function: b = v − (v − L)/n.

D. bid one penny above their own valuation to ensure they get the item.