From a mathematical point of view, the Schrödinger Equation is a LINEAR partial differential equation, as is a partial differential equation that is defined by a linear polynomial in the solution and its derivatives.
For a linear differential equation, if you got two different solutions
and
, then the linear combination
, where
and
are scalars, is also a solution.
This also is valid for only one solution (think of the other solution as equal to zero,
). So, as the Schrödinger Equation is a Linear partial differential equation, then if
is a solution, then
must also be a solution.
This is extremely important for physicist, as let us know that the superposition principle is valid.
Answer:
n = 3
Solution:
Since, the slit used is same and hence slit distance 'x' will also be same.
Also, the wavelengths coincide,
will also be same.
Using Bragg's eqn for both the wavelengths:
![xsin\theta = n\lambda](https://tex.z-dn.net/?f=xsin%5Ctheta%20%3D%20n%5Clambda)
(1)
![xsin\theta = (n + 1)\lambda](https://tex.z-dn.net/?f=xsin%5Ctheta%20%3D%20%28n%20%2B%201%29%5Clambda)
(2)
equate eqn (1) and (2):
![n\times 680.0\times 10^{- 9} = (n + 1)\times 510.0\times 10^{- 9}](https://tex.z-dn.net/?f=%20n%5Ctimes%20680.0%5Ctimes%2010%5E%7B-%209%7D%20%3D%20%28n%20%2B%201%29%5Ctimes%20510.0%5Ctimes%2010%5E%7B-%209%7D)
![n = \frac{510.0\times 10^{- 9}}{680.0\times 10^{- 9} - 510.0\times 10^{- 9}}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B510.0%5Ctimes%2010%5E%7B-%209%7D%7D%7B680.0%5Ctimes%2010%5E%7B-%209%7D%20-%20510.0%5Ctimes%2010%5E%7B-%209%7D%7D)
n = 3
Answer:19.34 miles
Explanation:
Given
First car travels with 32 mi/h
second travels with 54 mi/h
they leave at 2:00 Pm at 45
distance traveled by them is 0.5 hr
suppose First is traveling towards x axis and another travels 45 to it
Distance traveled by first car is ![32\times 0.5=16 miles](https://tex.z-dn.net/?f=32%5Ctimes%200.5%3D16%20miles)
Position vector of first car after 0.5 hr
![\vec{r_1}=32\times 0.5(\cos (45)\hat{i})](https://tex.z-dn.net/?f=%5Cvec%7Br_1%7D%3D32%5Ctimes%200.5%28%5Ccos%20%2845%29%5Chat%7Bi%7D%29)
Position vector of second car after 0.5 hr
![\vec{r_2}=54\times 0.5(\cos (45)\hat{i}+\sin (45)\hat{j})](https://tex.z-dn.net/?f=%5Cvec%7Br_2%7D%3D54%5Ctimes%200.5%28%5Ccos%20%2845%29%5Chat%7Bi%7D%2B%5Csin%20%2845%29%5Chat%7Bj%7D%29)
distance between them
![\vec{r_{21}}=27(\cos (45)\hat{i}+\sin (45)\hat{j})-16(\cos (45)\hat{i})](https://tex.z-dn.net/?f=%5Cvec%7Br_%7B21%7D%7D%3D27%28%5Ccos%20%2845%29%5Chat%7Bi%7D%2B%5Csin%20%2845%29%5Chat%7Bj%7D%29-16%28%5Ccos%20%2845%29%5Chat%7Bi%7D%29)
![\vec{r_{21}}=3.09\hat{i}+27\hat{j}\sin (45)](https://tex.z-dn.net/?f=%5Cvec%7Br_%7B21%7D%7D%3D3.09%5Chat%7Bi%7D%2B27%5Chat%7Bj%7D%5Csin%20%2845%29)
distance between them![|\vec{r_{21}}|=19.34](https://tex.z-dn.net/?f=%7C%5Cvec%7Br_%7B21%7D%7D%7C%3D19.34)
If a main sequence star is cooling and expanding, it is entering the red giant stage. This means that the star has burned up all of it's hydrogen and is now starting to burn its helium making it cooler.
ببيع ما عندي رصيد انا ما في رصيد شي عندي شغل رصيد انا ما في شي ما عندي عندي شي عندي شغل عنما في رصيد عندي