Recalling the energy formula
I’m thinking about the energy levels in a one-dimensional infinite potential well, specifically the ground state, using En=2mL2n2π2ℏ2.
Calculating energy
I’m noting the constants: electron mass, ℏ, and well width. Substituting these into E1=2mL2π2ℏ2 for the ground state energy.
Tackling the denominator
I’m resolving the denominator by multiplying the electron mass, well width squared, and factoring in π, reaching 7.2872×10−50.
Calculating energy
I’m working through the numerator and denominator, factoring in π2. The energy calculation focuses on the correctness of constants and coefficients, resulting in approximately 1.5×10−18 J.
Refining the expression
I’m honing the energy formula, ensuring precise constants and coefficients, and arriving at a simplified expression for E1 in joules.
Crunching the numbers
I’m carefully multiplying and simplifying the expressions for the numerator and denominator, ensuring precision with constants and coefficients, and ultimately calculating the ground state energy E1 in joules.
Converting energy
OK, let me see. I’m mapping the ground state energy from joules to electron volts by dividing by the electron charge, confirming the outcome is around 9.4 eV.
Converting energy
I’m verifying the calculated ground state energy of around 9.4 eV by cross-checking typical formulas for infinite wells and noting consistency with known constants and electron charge.
Thought about 电子在方势阱中的能量 for 28 seconds