Question

10,000 alpha particles per minute are passing through a straight tube of radius r. The resulting
electric current is approximately:
(A) 0.5 x 10^-16
amp
(B) 2 x 10^12
amp
(C) 0.5 x 10^12 amp.
(D) 2 x 10^-12 amp
.​

Answer 1

Given

10,000 alpha particles per minute are passing through a straight tube of radius r

To Find

The resulting  electric current is approximately

Solution

We know that

Charge (q) on one alpha particle is

$\sf \longrightarrow q = 3.2 \times 10^{-16} \ C$

Given that

10,000 alpha particles per minute are passing through a straight tube of radius r

Hence

The total charge (q') passing through the straight tube within 1 minute is

$\sf \longrightarrow q' = 10,000 \times 3.2 \times 10^{-16} \ C$

$\sf \longrightarrow q' = 3.2 \times 10^{-15} \ C$

We know that

$\sf \longrightarrow I=\dfrac{q'}{t}$

Here

• I = current

• q' = current

• t = time

Given that

10,000 alpha particles per minute are passing through a straight tube of radius r

Hence

• t = 60 s

We found out that

• q' = 3.2 x 10⁻¹⁵ C

Substituting the values

We get

$\sf \longrightarrow I=\dfrac{3.2 \times 10^{-15}}{60} \ Amp$

On further simplification

We get

$\sf \longrightarrow I=0.5 \times 10^{-16} \ Amp$

Hence

Current = 0.5 x 10⁻¹⁶ Amp

Therefore

Option (A) is correct

Answer 2

$\huge\rm\pink { ☆_!! Question !_! ☆}$

10,000 alpha particles per minute are passing through a straight tube of radius r. The resulting

electric current is approximately:

$\tt (A) 0.5 \times 10 ^{ - 16} amp$

$\tt (B) 2 \times 10 ^{ 12} amp$

$\tt (C) 0.5 \times 10 ^{ 12} amp$

$\tt (A) 2 \times 10 ^{ - 12} amp$

$\huge\rm \pink { ☆_!! Answer !_! ☆}$

$\tt (A) 0.5 \times 10 ^{ - 16} amp$ ☑️

$\huge\rm\pink { ☆_!! Solution !_! ☆}$

$\begin{gathered}\begin{gathered}\bf\gray{Given}\begin{cases}\sf\blue{10,000 \: alpha \: particles }\\\sf\green{1 min \: passing \: through \: straight \: tube \: of \: radius , r } \end{cases}\end{gathered}\end{gathered}$

⠀

$\begin{gathered}\begin{gathered}\bf\gray{To \: find}\begin{cases}\sf\red{ resulting \: electric \: current \: is \: approximately} \end{cases}\end{gathered}\end{gathered}$

⠀

As we know , $\tt current \: = \dfrac{charge}{time}$

⠀

• Current ↝ I

• Charge ↝ Q

• Time ↝T

⠀

★ charge of 1 Alpha particle ↝ +2

so , charge of 10000 Alpha particles

↝$\tt 10000 \times 2 \times 1.6 \times {10}^{ - 19}$

↝$\tt 20000 \times 1.6 \times {10}^{ - 19}$

⠀

Now according to the question → 10,000 alpha particles per minute are passing through a straight tube of radius r. , So time ↝1 min = 60 sec

⠀

$\tt Current (I)= \dfrac{20000×1.6× 10^{-19}}{60}$

⠀

After solving it ......✍️

⠀

$\tt Current (I)= 0.5×{10}^{-19}$