Recent content by yango_17

Thanks!

Homework Statement a) An electron is trapped in a one-dimensional box that is 526 nm wide. Initially, it is in the n=2 energy level, but after a photon is absorbed the electron is in the n=7 energy level. What is the wavelength of absorbed photon? b) Eventually, the electron ends up in the...

Homework Statement If enough of a monoprotic acid is dissolved in water to produce a 0.0153 M solution with a pH of 6.31, what is the equilibrium constant, Ka, for the reaction? Homework EquationsThe Attempt at a Solution I have attempted to solve this problem using ICE tables, but keep getting...

Span: Consider the vectors ##\vec{v_{1}},...,\vec{v_{m}}## in ##\mathbb{R}^{n}##. The set of all linear combinations ##c_{1}\vec{v_{1}}+...+c_{m}\vec{v_{m}}## of the vectors ##\vec{v_{1}},...,\vec{v_{m}}## is called their span: ##span(\vec{v_{1}},...,\vec{v_{m}})=\left \{...

You can rewrite span as the image of a matrix, since the image of a matrix is the span of its columns. Since image is a subspace, then does it follow that span is a subspace?

Homework Statement Consider the vectors ##\vec{v_{1}},\vec{v_{2}},...,\vec{v_{m}}## in ##\mathbb{R}^{n}##. Is span ##(\vec{v_{1}},...,\vec{v_{m}})## necessarily a subspace of ##\mathbb{R}^{n}##? Justify your answer. Homework EquationsThe Attempt at a Solution I understand the three conditions...

So, the properties would be that the set needs to contain the zero vector, needs to be closed under scalar multiplication, and needs to be closed under addition. When you say take arbitrary members of the set to test the last two properties, what exactly do you mean?

Homework Statement Is the set ##W## a subspace of ##\mathbb{R}^{3}##? ##W=\left \{ \begin{bmatrix} x\\ y\\ z \end{bmatrix}:x\leq y\leq z \right \}## Homework EquationsThe Attempt at a Solution I believe the set is indeed a subspace of ##\mathbb{R}^{3}##, since it looks like it will satisfy...

Ah, that's a great hint. Alright, I'll see how far I can take it from here

Homework Statement A realistic capacitor is almost always filled with dielectric, but invariably this dielectric will conduct just a little, and the charge stored on the capacitor's plates will "leak." Over time, quite a bit of current can leak away. A good capacitor has a small leakage...

Factoring out the radical i mean

I've arrived at ##\sqrt{2a^{2}+b^{2}}(\frac{1}{a}e^{at}-\frac{1}{a})## by factoring out the 1/a

Could x be replaced by ##(l_{0}-r)##?

He told us to assume initial length as ##l_{0}##. So, therefore, I'm thinking we can represent this system as ##\frac{1}{-4\pi\varepsilon _{0}} \frac{q^{2}}{r^{2}}+\mathbf{E}=-kx##. Does this seem reasonable?

Yes! I'm assuming ##\sqrt{2a^{2}+b^{2}} ## can be pulled out of the integral and we just have to integrate e^{at}. Doing this integral from 0 to t, I obtained ##\frac{1}{a}e^{at}\sqrt{2a^{2}+b^{2}}-\frac{1}{a}\sqrt{2a^{2}+b^{2}}##. Does this seem reasonable?