1.3 Check that the ratio ke2/G <math><msub><mrow><mrow><mi mathvariant="bold-italic">m</mi></mrow></mrow><mrow><mrow><mi mathvariant="bold-italic">e</mi></mrow></mrow></msub><msub><mrow><mrow><mi mathvariant="bold-italic">m</mi></mrow></mrow><mrow><mrow><mi mathvariant="bold-italic">p</mi></mrow></mrow></msub></math> is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

1.3 The units of the given equation ke2Gmemp ise = Electric charge in Ck = 14π?0 in N m2C-2, where ?0 = Permittivity of free space = 8.854 ×10-12 C2N-1 m-2G = Gravitational constant = N m2kg-2me=massofelectroninkg,mp=massofprotoninkgThereforeke2Gmemp = Nm2C-2×[C2]Nm2kg-2kg[kg]= M0L0T0So the given equation is dimensionlessWe have the following valuese = 1.6 ×10-19 CG = 6.67 ×10-11Nm2kg-2 kgme=9.1×10-31 kgmp=1.66×10-27The numerical value of this ratio is given byke2Gmemp = Nm2C-2×[C2]Nm2kg-2kg[kg] = 14π?0 = ×e2Gmemp= 14×π×8.854×10-12 ×(1.6×10-19)26.67×10-11×9.1×10-31×1.66×10-27 = 2.284×1039

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Physics Ncert Solutions Class 12th Physics Class 12th Electric Charges and Fields

1.3 Check that the ratio ke2/G $m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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alok kumar singh | Contributor-Level 10

3 months ago

1.3 The units of the given equation

$\frac{{k e}^{2}}{G m_{e} m_{p}}$ is

e = Electric charge in C

k = $\frac{1}{4 π ?_{0}}$ in N $m^{2} C^{- 2},$ where $?_{0}$ = Permittivity of free space = 8.854 $\times 10^{- 12}$ $C^{2} N^{- 1}$ $m^{- 2}$

G = Gravitational constant = N

$m^{2} {k g}^{- 2}$

$m_{e} = m a s s o f e l e c t r o n i n k g, m_{p} = m a s s o f p r o t o n i n k g$

Therefore

$\frac{{k e}^{2}}{G m_{e} m_{p}}$ = $\frac{[N m^{2} C^{- 2}] \times [C^{2}]}{[N m^{2} {k g}^{- 2}] [k g] [k g]}$ = $M^{0} L^{0} T^{0}$

So the given equation is dimensionless

We have the following values

e = 1.6 $\times 10^{- 19}$ C

G = 6.67 $\times 10^{- 11}$ ${Nm}^{2} {k g}^{- 2}$ kg

$m_{e} = 9.1 \times 10^{- 31}$ kg

$m_{p} = 1.66 \times 10^{- 27}$

The numerical value of this ratio is given by

$\frac{{k e}^{2}}{G m_{e} m_{p}}$ = $\frac{[N m^{2} C^{- 2}] \times [C^{2}]}{[N m^{2} {k g}^{- 2}] [k g] [k g]}$ = $\frac{1}{4 π ?_{0}}$ = $\times \frac{e^{2}}{G m_{e} m_{p}}$ =
$\frac{1}{4 \times π \times 8.854 \times 10^{- 12}}$ $\times \frac{{(1.6 \times 10^{- 19})}^{2}}{6.67 \times 10^{- 11} \times {9.1 \times 10^{- 31} \times 1.66 \times 10^{- 27}}_{}}$

= 2.284 $\times 10^{39}$

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1.3 Check that the ratio ke2/G $m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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1.3 Check that the ratio ke2/G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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1.3 Check that the ratio ke2/G $m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?