What are the units for effective mass in the formula m* = (h/2pi)2(d2E/dk2)-1?

AI Thread Summary
The discussion clarifies that the effective mass (m*) in the formula m* = (h/2pi)²(d²E/dk²)⁻¹ is indeed measured in kilograms (kg). The units of Planck's constant (h) are in joule-seconds (J-s), and energy (E) is in joules (J). Through unit analysis, it is shown that the formula simplifies correctly to yield kg for effective mass. The confusion arises from the cancellation of units, specifically how k, which has units of inverse length, interacts with the other terms. Ultimately, the effective mass is confirmed to have the correct unit of kg.
magnifik
Messages
350
Reaction score
0
Are the units for effective mass in kg? I have been trying to wrap my head around the concept then realized I wasn't even sure about the units.

The formula is: m* = (h/2pi)2(d2E/dk2)-1

the units of h are in J-s, and the units of E are in J so...
(J-s)2/J = J-s2
J = kg m2/s2
kg m2 s2/s2 = kg m2

why am i left with a m2 unit??
 
Physics news on Phys.org
k has units of inverse length. You have a k^2 in the numerator, which has units of m^-2, which will cancel the m^2, and leave you with m* having units of kg, which is correct.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Conversion factor when converting from SI to natural units
Replies
1
Views
794
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
1K
How do you derive the units for momentum for photons
Replies
4
Views
1K
Finding slip-off angle for mass off of sphere?
Replies
7
Views
1K
What is the problem with the units in this state equation of a gas?
Replies
12
Views
1K
Solving SI Unit Analysis: Force & Area
Replies
3
Views
6K
Rotational Motion Question, lever arm with two masses
Replies
2
Views
2K
Understanding Units of Force (Newtons and Pascals)
Replies
4
Views
2K
What are the units for the slope in an Acceleration vs Mass Graph?
Replies
3
Views
3K
Attempting to teach this: Momentum and Impulse
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top