Consider an electron that is 10^-10 m from an alpha particle (q = +3.2 times 10^-19 c). (a) what is the electric field due to the alpha particle at the location of the electron? (b) what is the electric field due to the electron at the location of the alpha particle? (c) what is the electric force on the alpha particle? on the electron?

(a) 2.88×10¹¹ N/C.

(b) 1.442×10¹⁰ N/C

(c) 46.14×10⁻⁹ N

Explanation:

(a) Electric field due to alpha particle at the location of the electron

E = Kq/r² Equation 1

Where E = Electric field, q = charge of the alpha particle, K = proportionality constant, r = distance between the electron and the alpha particle.

Given: q = 3.2×10⁻¹⁹ C, r = 10⁻¹⁰ m.

Constant: K = 9×10⁹ Nm²/C²

Substituting into equation 1

E = 9×10⁹(3.2×10⁻¹⁹)/(10⁻¹⁰)²

E = 28.8×10⁻¹⁰/10⁻²⁰

E = 2.88×10¹¹ N/C.

(b) Electric Field due to the electron at the location of the alpha particle

E₁ = Kq₁/r² Equation 2

Where,

E₁ = Electric Field due to the electron at the location of the alpha particle.

q₁ = charge of an electron.

Given: r = 10⁻¹⁰ m

Constant: K = 9×10⁹ Nm²/C², q₁ = 1.602×10⁻¹⁹ C

Substituting into equation 2

E₁ = 9×10⁹×1.602×10⁻¹⁹/(10⁻¹⁰ )²

E₁ = 14.42×10⁻¹⁰/10⁻²⁰

E₁ = 14.42×10¹⁰

E₁ = 1.442×10¹⁰ N/C.

(c) The electric force on the alpha particle and on the electron.

F = Kqq₁/r² Equation 3

Given: q = 3.2×10⁻¹⁹ C, r = 10⁻¹⁰ m,

Constant:  K = 9×10⁹ Nm²/C², q₁ = 1.602×10⁻¹⁹ C

Substituting these values into equation 3

F =9×10⁹( 3.2×10⁻¹⁹ )(1.602×10⁻¹⁹)/(10⁻¹⁰)²

F = 46.14×10⁻²⁹/10⁻²⁰

F = 46.14×10⁻⁹ N

Thus the electric force = 46.14×10⁻⁹ N

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂