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

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SUMMARY

The effective mass (m*) in the formula m* = (h/2pi)²(d²E/dk²)⁻¹ is definitively measured in kilograms (kg). The discussion clarifies that 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 established that the final units for effective mass simplify correctly to kg after accounting for the units of k, which are in inverse length (m⁻²), effectively canceling out the m² in the numerator.

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magnifik
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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??
 
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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.
 

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