You have a block of an unknown metal. Which properties would be most helpful in determining what it is? If it could be

one of your classmates is having trouble understanding ions, he explain the formation of a cation like this: "when you add an el

Irina-Kira [14]

Electrons carry a negative charge, so when you add on to the electron, the ion gets more negative.
hope this helps!

8 0

3 years ago

German physicist Werner Heisenberg related the uncertainty of an object\'s position (Δx) to the uncertainty in its velocity Δv.

Assoli18 [71]

Heisenberg's Uncertainty Principle gives a relationship between the standard deviation of an object's position and its momentum.

$\Delta p \cdot \Delta x = h / (4 \pi)$ where

$\Delta p$ the standard deviation of the object's momentum,
$\Delta x$ the standard deviation of the object's position, and
$h \approx 6.63 \times 10^{-34} \; \text{J} \cdot \text{s}$ the Planck's constant.

By definition, the momentum of the electron equals the product of its mass and velocity.

$p = m\cdot v$

Assuming that measurement of the mass of the electron $m$ is accurate. It is assumed to be a coefficient of constant value. The standard deviation in the electron's velocity is thus directly related to that of its mass. That is:

$\Delta p = m \cdot \Delta v$

$\Delta v = 0.01 \times 10^{6} \;\text{m}\cdot \text{s}^{-1}$ from the question;

$\Delta p = m\cdot v \\ \phantom{\Delta p} = 0.01 \times 10^{6} \; \text{m} \cdot \text{s}^{-1} \times 9.11 \times 10^{-31} \; \text{kg}\\\phantom{\Delta p} = 9.11 \times 10^{-27} \; \text{kg} \cdot \text{m}\cdot \text{s}^{-1}$

Convert the unit of the Planck's constant to base SI units (kg, m, s, etc.) if it was provided in derived units such as joules. Doing so would allow for a dimension analysis on the accuracy of the result.

$h = 6.63 \times 10^{-34} \; \text{J} \cdot \text{s}\\\phantom{h} = 6.63 \times 10^{-34} \; (\text{N}\cdot \text{m}) \cdot \text{s} \\\phantom{h} = 6.63 \times 10^{-34} \; ((\text{kg} \cdot \text{m}\cdot \text{s}^{-2}) \cdot \text{m}) \cdot \text{s}\\\phantom{h} = 6.63 \times 10^{-34} \; \text{kg} \cdot \text{m}^{2} \cdot \text{s}^{-1}$

Apply the Uncertainty Principle:

$\Delta x = h/ (4 \pi \cdot \Delta p)\\\phantom{\Delta x} = 6.63 \times 10^{-34} \; \text{kg} \cdot \text{m}^{2} \cdot \text{s}^{-1} / (4 \pi \cdot 9.11\times 10^{-27} \; \text{kg} \cdot \text{m}\cdot \text{s}^{-1})\\\phantom{\Delta x} = 5.79 \times 10^{-9} \; \text{m}$ .