Answer:
I guess that the atoms are:
Protons: 6 8 5 2 12 12
Neutrons: 8 8 5 3 13 14
Now, two atoms are isotopes if they share the same number of protons (so both atoms are the same element) but they have a different number of neutrons.
From the given options, the only two that have the same number of protons but a different number of neutrons are:
Protons 12, neutrons 13
and
Protons 12, neutrons 14.
These two are isiotopes.
(a) 392 N/m
Hook's law states that:
(1)
where
F is the force exerted on the spring
k is the spring constant
is the stretching/compression of the spring
In this problem:
- The force exerted on the spring is equal to the weight of the block attached to the spring:

- The stretching of the spring is

Solving eq.(1) for k, we find the spring constant:

(b) 17.5 cm
If a block of m = 3.0 kg is attached to the spring, the new force applied is

And so, the stretch of the spring is

And since the initial lenght of the spring is

The final length will be

Answer:

Explanation:
A function f(x) is a Probability Density Function if it satisfies the following conditions:

Given the function:

(1)p(x) is greater than zero since the range of exponents of the Euler's number will lie in 
(2)
![\int_{0}^{\infty} p(x)=\int_{0}^{\infty} \dfrac{1}{r}e^{-x/r}\\=\dfrac{1}{r} \int_{0}^{\infty} e^{-x/r}\\=-\dfrac{r}{r}\left[e^{-x/r}\right]_{0}^{\infty}\\=-\left[e^{-\infty/r}-e^{-0/r}\right]\\=-e^{-\infty}+e^{-0}\\SInce \: e^{-\infty} \rightarrow 0\\e^{-0}=1\\\int_{0}^{\infty} p(x)=1](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20p%28x%29%3D%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20%5Cdfrac%7B1%7D%7Br%7De%5E%7B-x%2Fr%7D%5C%5C%3D%5Cdfrac%7B1%7D%7Br%7D%20%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20e%5E%7B-x%2Fr%7D%5C%5C%3D-%5Cdfrac%7Br%7D%7Br%7D%5Cleft%5Be%5E%7B-x%2Fr%7D%5Cright%5D_%7B0%7D%5E%7B%5Cinfty%7D%5C%5C%3D-%5Cleft%5Be%5E%7B-%5Cinfty%2Fr%7D-e%5E%7B-0%2Fr%7D%5Cright%5D%5C%5C%3D-e%5E%7B-%5Cinfty%7D%2Be%5E%7B-0%7D%5C%5CSInce%20%5C%3A%20e%5E%7B-%5Cinfty%7D%20%5Crightarrow%200%5C%5Ce%5E%7B-0%7D%3D1%5C%5C%5Cint_%7B0%7D%5E%7B%5Cinfty%7D%20p%28x%29%3D1)
The function p(x) satisfies the conditions for a probability density function.
Answer:
b.
Explanation:
In case of Single Slit, diffraction will occur.
Then In Single slit Diffraction, width of central fringe is

where D= distance b/w screen and slit
a= slit width
\lambda = wavelength
Thus if Screen width increases keeping other factors same then width of central fringe becomes narrower as

On increasing the slit width the central bright fringe width The width of the central bright fringe becomes narrower.