Homework Statement
I have a shape about the origin. It has rotational symmetry but not reflectional symmetry (its an odd star shape!).
I have to write down in standard notation the elements of the symmetry group and I have to construct a caley table under composition of symmetries.
I...
Write down the 3 principles underpinning Boltzmanns law and indicate which of these is incompatible with the quantum theory of gases
The Attempt at a Solution
Well I know two...
1. The conservation of energy
2. Equal probabilities of allowed configurations
But I'm a bit stuck...
I have been asked to find whether or not indistinguishability may or may not be ignored from a given sample of atoms at a given temperature.
The calculation I have done fine, but my question is given that the criterion for neglecting indistinguishability has to satisfy
de broglie...
Homework Statement
A quantum system has a measurable property represented by the observable S with possible eigenvalues nh, where n = -2, -1, 0, 1, 2. The corresponding eigenstates have normalized wavefunctions \psi_{n}. The system is prepared in the normalized superposition state given by...
Determine the possible outcomes of the measurement Sz for the two electrons
\psi = \frac{1}{2} (\psi_{+}(A)\psi_{-}(B)-\psi_{+}(A)\psi_{-}(B))
The Attempt at a Solution
Now I know how to work out the outcomes for each of the pairs, but what I'm not sure about is how to handle the...
Can someone tell me how the outer shell structure is determined from the electronic structure. I know i can look this up but I'd like to know how it is derived and are there any rules I should follow so i can determine them myself?
Is there a standard way of quoting uncertainties for say counting radioactive decay counts?
I know I can use sqrt(n)
And I know I can use fractional uncertainty 1/(sqrt(n)) too.
Is there a standard way of quoting? Apologies if this is in the wrong section
Can someone tell me how I find the speed of sound in air?
If I plot a graph of frequency against length would I be right in saying that I can find the speed of sound by finding where the two points on the graph intersect and multiplying by 2, so that
v = 2 * Lf
I need to find the indefinite integral
\int \frac{sec^2 (x)}{\sqrt{1-tan^2 (x)}}
Now, I'm not sure which method to use here.... I think that the quotient and the square root is confusing me here. I can certainly integrate the numerator - thats not the problem, I'm not sure how to...
Homework Statement
Find the indefinite integral of
\int \frac{sec^2 x}{\sqrt{1-tan^2 x}} dx
I'm stuck on how to proceed with the denominator. I know that
\sqrt{1+tan^2 x}
is equivalent to \\sec\theta
but I cant seen to find an equivalent to what I have. Can anyone give me...
Find the volume of the solid of revolution obtained when the region under the graph of
f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x}
from x = 1 to x = 6
Homework Equations
\pi \int (f(x))^2 dx
The Attempt at a Solution
Ok, the equation I gave above should be that...
I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign)
S (x - 2) Ln(3x)
I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used
f(x) =...
This question concerns 2 positively charges masses at a certain distance apart.
If I have a value for gravitational potential energy of
-3.6e-12 J
And a value for electrostatic potential energy of
3.6e-12 J
Would I be right in saying that the overall potential energy of the system...