a. A sculptor has asked you to help electroplate gold onto a brass statue. You know that the charge carriers in the ionic solution are singly ionized gold ions, and you've calculated that you must deposit 0.50 g of gold to reach the necessary thickness. How much current do you need, in mA, to plate the statue in 4.0 hours?
b. A metallic wire has a diameter of 4.12mm. When the current in the wire is 8.00A, the drift velocity is 5.40×10−5m/s. What is the density of free electrons in the metal?
c. A 1.3×10−3 V/m electric field creates a 4.4×1017 electrons/s current in a 1.4-mm-diameter aluminum wire. What is the drift speed? What is the mean time between collisions for electrons in this wire?
d. A 18-cm-long nichrome wire is connected across the terminals of a 1.5 V battery.What is the electric field inside the wire? What is the current density inside the wire? If the current in the wire is 2.0 A , what is the wire's diameter?
answer) a) first we have to find number of moles in gold atoms
number of moles=0.50g/196.9666g/mole=0.002539 mole
so the number of atoms =0.002539*6.022*1023=1.52869*1021atoms
now charge =1.52869*1021*1.6*10-19C=244.5897 C
now we have the formula
I=Q/t=244.5897C/4*3600 s=16.99 mA
so the answer is 17 mA or 17.0 mA
b) for density we have the formula
n=I/qvA
A=pir2
r=d/2=4.12mm/2=2.06mm=2.06*10-3m
so now putting all the values in above eqn
n=8/1.60*10-19*5.4*10-5m/s*pi*(2.06*10-3)2=6.95*1028m-3
so the answer is 6.9*1028m-3 or 7.0*1028m-3 or 6.95*1028m-3
d) here we have the formula
E=V/m=1.5/0.18m=8.3 V/m
so the electric field is 8.3 V/m or 8.33 V/m
we have the formula for current density=E=8.33V/m*6.7*105ohm-1m-1=5.6*106
A/m2
so the current density=5.6*106A/m2 or 5.58*106A/m2
the wire diameter
we have the formula
current density=current/A
A=Current/Current density=2.0/5.58*106
pir2=2/5.58*106
r2=11.407997*10-8
r=3.38*10-4m
d=2r=6.76*10-4m
so diameter=6.8*10-4m or 6.76*10-4m or 0.68 mm or 0.676mm
( for question c , i need the value for free electron density of aluminium which is missing)
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