The value of Planck's constant in SI unit is

Options

A. `6.63 xx 10^(-31)J-s`
B. `6.63 xx 10^(-30) kg-m//s`
C. `6.63 xx 10^(-32) kg-m^(2)`
D. `6.63 xx 10^(-34) J-s`

Explanation

To find the value of Planck's constant in SI units, we can follow these steps:

### Step 1: Identify the value of Planck's constant
Planck's constant is denoted by \( h \) and its value is given as \( 6.63 \times 10^{-34} \).

### Step 2: Determine the unit of Planck's constant
To find the unit of Planck's constant, we can use the relationship between energy, wavelength, and speed of light. The equation is given by:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( E \) is energy (in joules),
- \( h \) is Planck's constant,
- \( c \) is the speed of light (in meters per second),
- \( \lambda \) is the wavelength (in meters).

### Step 3: Rearranging the equation to solve for \( h \)
From the equation, we can rearrange it to express \( h \):

\[ h = \frac{E \cdot \lambda}{c} \]

### Step 4: Substitute the units into the equation
Now, we substitute the units into the equation:
- The unit of energy \( E \) is joules (J),
- The unit of wavelength \( \lambda \) is meters (m),
- The unit of speed of light \( c \) is meters per second (m/s).

### Step 5: Write down the units
Substituting these units into the equation for \( h \):

\[ \text{Unit of } h = \frac{\text{J} \cdot \text{m}}{\text{m/s}} \]

### Step 6: Simplify the units
Now, simplify the units:

\[ \text{Unit of } h = \frac{\text{J} \cdot \text{m}}{\text{m/s}} = \text{J} \cdot \text{s} \]

### Step 7: Final result
Thus, the unit of Planck's constant \( h \) is joule seconds (J·s). Therefore, the value of Planck's constant in SI units is:

\[ h = 6.63 \times 10^{-34} \text{ J·s} \]

### Final Answer
The value of Planck's constant in SI units is \( 6.63 \times 10^{-34} \text{ J·s} \).

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