1. Calculate the de Broglie wavelength in picometers (1 picometer =10^−12 meters) of an electron that has kinetic energy of 10 keV. The mass of an electron is 9.11 x 10^−31 kg
2. Winter is coming, so I want to make a 1500 W heating coil which will plug into a 120 V wall outlet. The coil will have a cross sectional area of 0.01 cm^2 and a length (when fully unwound) of 5 m.
Determine the resistivity of the coil required, in Ωcm:
3. At 300 K we see the electron concentration in the conduction band for pure (undoped) Si is 10^10/cm^3. How many electrons per Si atom is this? You can use scientific notation, as in A.AAeB
Si is diamond cubic with 8 Si atoms per unit cell and a lattice parameter of 0.543 nm.
help me with plzzz
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KE=10⁴•1.6•10⁻¹⁹ =1.6•10 ⁻¹⁵J
KE=mv²/2 =m²v²/2m =p²/2m =>
p=sqrt(2m•KE)
λ=h/p =h/sqrt((2m•KE)=
=6.63•10⁻³⁴/sqrt(2•9.1•10 ⁻³¹•1.6•10 ⁻¹⁵)=
=1.22•10⁻¹¹ m=0.122 pm
-------
R=ρL/A
P= U²/R= U²A/ ρL
ρ= U²A/ PL =
=120²•10⁻²/1500•500=1.92•10⁻⁴Ω•cm
0.122 is wrong......is that the full answer? are you missing something? the computer says it is wrong.
1. To calculate the de Broglie wavelength of an electron, we can use the formula:
λ = h / p
where λ is the de Broglie wavelength, h is Planck's constant (6.626 x 10^-34 J.s), and p is the momentum of the electron.
The momentum of an object can be calculated using the formula:
p = sqrt(2 * m * E)
where m is the mass of the electron and E is the kinetic energy.
Given:
Mass of an electron (m) = 9.11 x 10^-31 kg
Kinetic energy (E) = 10 keV = 10 x 10^3 eV = 10 x 10^3 x 1.6 x 10^-19 J
First, convert the kinetic energy from eV to Joules using the conversion factor 1 eV = 1.6 x 10^-19 J. Then substitute the values into the equation to find the momentum. Finally, use the momentum to calculate the de Broglie wavelength.
2. To determine the resistivity of the heating coil, we can use Ohm's Law:
R = V / I
where R is the resistance, V is the voltage, and I is the current. Rearrange the equation to solve for resistance:
R = V / I
Given:
Voltage (V) = 120 V
Power (P) = 1500 W
Cross-sectional area (A) = 0.01 cm^2 = 0.01 x 10^-4 m^2
Length (L) = 5 m
First, calculate the current using the formula:
P = V * I.
Then, use the current and given values to calculate the resistance:
R = V / I
3. To find the number of electrons per Si atom given the electron concentration in the conduction band of pure Si, we can use the relationship between electron concentration and lattice parameters.
The electron concentration (n) in a material is given by:
n = N / V
where N is the number of electrons and V is the volume of the material.
The volume of one Si atom can be calculated using the lattice parameter (a) of Si, which is given as 0.543 nm. The volume of the unit cell (V_cell) can be calculated using the formula:
V_cell = a^3
Given:
Electron concentration (n) = 10^10/cm^3
Lattice parameter (a) = 0.543 nm
Number of Si atoms per unit cell = 8
First, convert the electron concentration from cm^-3 to m^-3. Then, calculate the volume of one Si atom using the lattice parameter. Finally, divide the electron concentration by the volume of one Si atom to find the number of electrons per Si atom.