1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Goryan [66]
3 years ago
8

An ensemble of 100 identical particles is sent through a Stern-Gerlach apparatus and the z-component of spin is measured. 46 yie

ld the value +\frac{\hbar}{2}+ ℏ 2 while the other 54 give -\frac{\hbar}{2}− ℏ 2. Compute the standard deviation of the measurements.
Mathematics
1 answer:
Elodia [21]3 years ago
4 0

Answer:

The standard deviation is 0.4984 \hbar

Step-by-step explanation:

In order to find standard deviation, The equation is given as

\sigma=\sqrt{\frac{1}{n} \sum_{i=1}^{100} (\mu-x_i)^2

Here μ is the mean which is calculated as follows

                                       \mu=\frac{\sum_{i=1}^{100} x_i}{n}\\\mu=\frac{46\times \frac{\hbar}{2}+54\times \frac{-\hbar}{2}}{100}\\\mu=\frac{-4 \hbar}{100}\\\mu=-0.04 \hbar

Now the standard deviation is given as

                      \sigma=\sqrt{\frac{1}{100} \sum_{i=1}^{100} (-0.04 \hbar-x_i)^2}\\\sigma=\sqrt{\frac{1}{100} [[46 \times(-0.04 \hbar-0.5 \hbar)^2]+[54 \times(-0.04 \hbar+0.5 \hbar)^2]}]\\\sigma=\sqrt{\frac{1}{100} [[46 \times(-0.54 \hbar)^2]+[54 \times(0.46 \hbar)^2]}]\\\sigma=\sqrt{\frac{1}{100} [[46 \times(0.2916 \hbar)]+[54 \times(0.2116 \hbar)]}]\\\sigma=\sqrt{\frac{1}{100} [13.4136 \hbar+11.4264 \hbar}]\\\sigma=\sqrt{\frac{24.84 \hbar}{100}}\\\sigma =0.4984 \hbar

So the standard deviation is 0.4984 \hbar

You might be interested in
What is the most common weight?" 10 points This dot plot shows the weights of backpacks, in kilograms, of 50 sixth-grade student
svetoff [14.1K]

Answer:

4

Step-by-step explanation:

i think its correct

5 0
3 years ago
What is the value of x?
Nat2105 [25]
I think the answer would be B. 4 cm
5 0
3 years ago
Read 2 more answers
What are the coordinates of the turning point of the parabola whose equation is y=-x^2+4x+1
Arlecino [84]

Answer:

The maximum of the parabola lands at (2,5).

3 0
3 years ago
Find eah missing length to the nearest tenth
olga_2 [115]
Let’s go with 7.0 that is what I think it is
6 0
3 years ago
What is 10 tens minus 1 ten 1 tenth
Natasha2012 [34]
10*10-(1*10+1*\frac{1}{10})\\100-(10+\frac{1}{10})\\100-(\frac{100}{10}-\frac{1}{10})\\\frac{1000}{10}-(\frac{99}{10})\\\frac{901}{10}\\90.1

90.1
4 0
3 years ago
Other questions:
  • Match each expression with an equivalent expression.
    11·1 answer
  • Given f(x)=2x-3, find f(17).
    12·2 answers
  • PLEASE HELP!! I need this,i'd appreciate it! :3
    5·1 answer
  • Please help! 27 points!<br> answer correctly!
    11·1 answer
  • What is 7,452 divided by 54 in steps?
    12·2 answers
  • An urban planner examines police-report data for many cities and towns and discovers that cities with professional football team
    7·1 answer
  • Using the pythagorean theorem, calculate the length of the missing sides (c1, c2, c3)​
    13·1 answer
  • Idc anymore bc i got my answer XDD
    6·2 answers
  • Solve the inequality.<br><br> $x-4&lt;-5$<br><br> The solution is
    8·2 answers
  • 15.<br> How many values are in the data set whose histogram is shown below?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!